Big Numbers

The IIABA is the premier association for independent agents, representing more than a quarter million agents and their employees. In this lesson, you will learn how to communicate using large numbers in Spanish. Everyone has their own unique number sequence (in case you want to know yours), these numbers explain your life in terms of wealth,health and love. Welcome to my Large Number Site. Except for six, hold out your thumb and pinky. Create your own signs with impact! Download single numbers or take a file with all numbers 0-9 in a single download. In the 16th century, mathematician Gerolama. Read 73 reviews from the world's largest community for readers. Large Numbers Mixed Review : Place Value, Ordering, Before/After, Comparison, Number Name), Addition and Subtraction. The phrase "large number" has a subjective meaning, which is unsatisfactory for googologists because their studies rely on the definition of the term. A Uniform Random Number block connected to Compare To Constant block acts as a Bernoulli trial. Are 'a large number of' and 'large numbers of' used interchangeably? Which means more? 2. com with free online thesaurus, antonyms, and definitions. Following Scott's idea: Essentially your number 4. Yamaha WaveRunners. Remove Ads. Name brands you love at savings you can't deny. And Even MORE Practice with Scientific Notation (Boy, are you going to be good at this!) Positively positives! 41) What is the number of your street address in scientific notation?. Multiply the Big Numbers close to 10, 100, 1000, etc. In general, students have difficulty with two things when dealing with. law of large numbers: Statistical concept that larger the sample population (or the number of observations) used in a test, the more accurate the predictions of the behavior of that sample, and smaller the expected deviation in comparisons of outcomes. Large numbers going from 0-9 (four exemplars of each of number). Numbers are separated into groups: ones, tens, hundreds, thousands, millions, and so on. Place Value of a Number - powered by WebMath. Large numbers in the OT The exceedingly high numbers of the able-bodied men over the age of twenty conscripted into the armies of Israel, as recorded in Num 1; 26, continue to trouble modern scholars. FFT based multiplication of large numbers (Click here for a Postscript version of this page. The law of large numbers is a theorem from probability and statistics that suggests that the average result from repeating an experiment multiple times will better approximate the true or expected underlying result. If you are dealing with big numbers in your game, you might have encountered the issue of properly formatting them. This article lists and discusses the usage and derivation of names of large numbers, together with their possible extensions. They have told me quite a bit about these two numbers: the numbers are even and they are negative. R is for real numbers, rational or irrational (Ex. This method is known as scientific notation. This is a program for calculations with big natural numbers. Here's how a scientist, or a liberal arts major, might do it. as_completed, but taking an iterable instead of a list, and with a limited number of tasks running concurrently. The following table lists those names of large numbers that are found in many English dictionaries and thus have a claim to being "real words. It states that if you repeat an experiment independently a large number of times and average the result, what you obtain should be close to the expected value. The numbers may be very large (may not fit in long long int), the task is to find product of these two numbers. This lesson plan for teachers of older teenage and adult students at low intermediate B1 level is about big numbers. Each number on the left represents a power of ten 0 one 1 ten 2 hundred 3 thousand 6 million 9 billion 12 trillion 15 quadrillion 18 quintillion 21 sextillion. Bing helps you turn information into action, making it faster and easier to go from searching to doing. See these two examples where I calculate 13^18, Using LibreOffice Calc Using. An educational video for kids. Before things get totally out of hand, let's start by working our way up the still-fathomable powers of 10. Customizable Large Numbers clocks from Zazzle. Hexadecimal Numbers. The next step for your students is to practice until they become fluent and confident. Big Numbers by Jack Getze is the premiere offering in a mystery series about a wise-cracking stockbroker who can’t stay out of trouble, and who is just one step away from being a ‘broke’ stockbroker. In this case, the Customer Care team will remove your account from auto-renewal to ensure you are not charged for an additional year and you can continue to use the subscription until the end of your subscription term. Printable worksheets and online practice tests on Large Numbers for Grade 4. Sales data reported by PiperJaffray for the four weeks ending October 20 (when the Massachusetts emergency ban was in effect for 25 of the 28 days) and the four previous weeks (mostly before the ban went into effect) were compared to sales data for the previous year. It's a numbers song for children and adults. The idea is based on school mathematics. Let's find possible answers to "Enter in large numbers" crossword clue. Now select all the cells which needs to be converted. Super learning tool for schools. Kongregate [web version] List of Large Numbers, post your thoughts on the discussion board or read fellow gamers' opinions. k American European SI--Prefix -33 revo -30 tredo -27 syto -24 fito -21 ento -18 quintillionth atto -15 Quadrillionth femto -12 trillionth pico -9 Billionth nano -6 Millionth micro -3 Thousandth milli -2 Hundredth centi -1 Tenth deci 1 Ten deca 2 Hundred hecto 3 Thousand kilo 4 Myriad 6 Million Million mega 9 Billion Milliard giga 12 Trillion Billion. Locate any 만, 억, and 조. Gibson Research Corporation is owned and operated by Steve Gibson. A topic that always needs to be revised by any level of students. Hexadecimal Numbers. We made a fun place value dice game which we use with think boards to get your kids practicing saying big numbers. Scientific Notation To Decimal Converter online calculator. Ordering Numbers; Ordering Decimals; Ordering Games; Algebra, the next step after Numbers. Webmail Sign in. Download it once and read it on your Kindle device, PC, phones or tablets. Law of Large Numbers. 200mm High, 3mm thick, Brushed Stainless Steel House Numbers, Price Per Character. If you want to write down the value of a very big number (way bigger even than a googolplex ), the mathematical notations for factorial or exponentiation, the fastest growing 'conventional' functions, eventually becomes unweildy; you get too many factorials or exponents to manipulate easily. Palm Orientation: Your palm should always face away from your body when signing the numbers 30 through 99. Instead, it is the distance that light can travel in a year. House numbers. Our "Count to 100 Song" is a fun challenge for children who are learning big numbers! This is another great teaching supplement for teachers and parents who would like to practice some basic. (After your visit, close the MegaPenny Project window to return to Math Cats. The randomness comes from atmospheric noise, which for many purposes is better than the pseudo-random number algorithms typically used in computer programs. The law of large numbers (LLN) is a theorem from statistics. There are related clues (shown below. It was cute. In 1940, the mathematician Edward Kasner published the book "Mathematics and the Imagination", in which he popularized the words googol and googolplex which his nephew suggested as names for big numbers. Large Number. Y-axis = outcome; X-axis = time. Here's how a scientist, or a liberal arts major, might do it. Tags: X_Question. Our free number coloring pages have engaging pictures for each number that children can count and color at the same time. Adding large numbers (that is, multiple digit numbers) follows the same organizational principles as adding single digits. Now select all the cells which needs to be converted. Big Numbers Lyrics: Big numbers, big numbers / , that's a big number / Big numbers, big numbers / Whole team count it, that's a big number / Foreign cars, foreign broads / Foreign seats with the. Big_numbers is a library written in (Small)Eiffel which provides arbitary precision numbers. The law of large numbers, in probability and statistics, states that as a sample size grows, its mean gets closer to the average of the whole population. large number n noun : Refers to person, place, thing, quality, etc. more chances to win with bonus play. " The theorem roughly states that the larger a random sample is the more its mean will mirror that of the total population. Algebra Menu; Special Numbers. pipCalc is a command line calculator which can handle large numbers. Solid black numbers, print big numbers. com is THE Local Business Directory Including: Phone, Ratings and Reviews, Maps, Driving Directions, Address, Website, Hours of Operation and more. math package, called BigInteger and BigDecimal. Listen to the mp3-files for each exercise and type out or write down the sentences and numbers that you hear or answer the comprehension questions. Submitted by Walter Rader (Editor) from Sacramento, CA, USA on Aug 11 2009. In Excel the limit is 15 digits. Large numbers are numbers that are significantly larger than those ordinarily used in everyday life, for instance in simple counting or in monetary transactions. Numerals printed from web browser appear 6 and a half inches tall while PDF letters are eight inches high. It is very common for students to have difficulty with the numbers 11- 19. Scientific Notation is a shorthand way of writing really large numbers. I expect that is because although it takes fewer single digit calculations that one not as easy to explain in the number of words allowed. But this isn't algorithm the article eventually asserts is the most efficient. These are full-sheet sized letters and numbers. For many students, very big numbers are difficult to read. In the latest addition to the put-big-numbers-in-context genre, here’s the history timeline of…. They cost less. second chance drawings. Before things get totally out of hand, let's start by working our way up the still-fathomable powers of 10. In some problems, the number at the very bottom. It is one of the factors insurance companies use to determine their rates. Play along in a heartbeat. The numbers may be very large (may not fit in long long int), the task is to find product of these two numbers. Last page (page 9) The Knuth -yllion Notation. Customizable Large Numbers clocks from Zazzle. Law Of Large Numbers: In probability and statistics, the law of large numbers states that as a sample size grows, its mean gets closer to the average of the whole population. I mentioned an extremely large number in this comic, and then talked a little about comparing it to another large number in this blag post. Im facing a scenario where in ill have to compute some huge math expressions. The equivalent number will appear in the Results area. Sometimes a single number is the most important thing you want to track in your Power BI dashboard or report, such as total sales, market share year over year, or total opportunities. Printable worksheets and online practice tests on Large Numbers for Grade 6. game and winning number updates sent to you. Every time you click the New Worksheet button, you will get a brand new printable PDF worksheet on Large Numbers. Teaches how to write large Spanish cardinal numbers which are used for counting. About This Quiz & Worksheet. Tool to make a division with large numbers. Excel and really large numbers - they don't play nice together. The Big Numbers Song. A series of free printable math flash cards including numbers 1 to 100, 0's and various math symbols in a variety of fonts, colors and sizes for all your math teaching/learning activities. Some languages don't support currency translation. So that I can divide one big number into other 3 or 4 or 5 smaller numbers. Printing Has Made Life A Lot Easier. Japanese is based on the Chinese system which uses ten thousand as a basic unit. Combine the signs for the first and then second digit of the number to sign the numbers 30 through 99. more chances to win with bonus play. This is what the crowd is at a very large college football game. Improve the curb appeal of your house or commercial building with Architectural Address Numbers. The book, which Schwartz illustrated himself, takes readers on a visual tour of the number system — starting with small, relatable numbers and building to giant, unimaginable ones. Buy here your Large Number Signs. Then we multiply second digit of second. by Marco Taboga, PhD. Aurora Borealis February 18. For example, the number 500 000 000 000 000 000 000 can be called 5 x 10 20 in scientific notation since there are 20 zeros behind the 5. Big Numbers. Cardinal numbers describe the size of a collection of objects; two such collections have the same (cardinal) number of objects if their members can be matched in a one-to-one correspondence. Many of our low vision watches feature big faces and bold numbers for easy viewing, with your choice of white on black, black on white, or even yellow faces for maximum contrast. 3 Names of Large Numbers. The difference is, n and even n 2 grow in a more-or-less manageable way, but 2 n just shoots up off the screen. Tool to make multiplication with large numbers. सहस्र num one thousand (1,000) साहस्र mf(ī)n by a thousand, one thousand fold; numerous, infinite. 99% APR for 36 months & 3 Years Genuine Yamaha Coverade Or Up to $800 Off. Much better to use Binet's explicit formula. BigDecimal []. Finally, Pickover has defined a superfactorial function, n$, defined as follows: n$ = n!n! n! | {z } n! copies and even 3$ has an enormous number of digits. Large Clock Adhesive Numbers. With its graphic black and white design and large spaces for all your dates and appointments, Big Letters Big Numbers is easy for EVERYONE to read. The phrase "large number" has a subjective meaning, which is unsatisfactory for googologists because their studies rely on the definition of the term. Click here to report the issue. Video by KidsTV123. The numbers in that sequence are called the powers of 10. The opening weekend numbers aren't quite as big as its predecessor, but still huge for September. You cannot receive a refund if you have placed a ShippingPass-eligible order. There's a Large Numbers quiz for everyone. This interactive applet is part of the online content for Introduction to the Practice of Statistics, 8th Edition (Moore and McCabe). And Even MORE Practice with Scientific Notation (Boy, are you going to be good at this!) Positively positives! 41) What is the number of your street address in scientific notation?. Googology is the study and nomenclature of large numbers. This is the case because 100 is a reasonably large sample size (for coin flipping), so we expect the results to be close to 50:50. 000 are OK, but as you go larger, you'll run out of space quickly. Like 'a lot of' and 'lots of', are 'a large number of' and 'large numbers of' used before uncountables as well as plurals?. Super learning tool for schools. Montessori Math: Add & Subtract Large Numbers uses some very interesting, systematic visual and organizational clues to help kids grasp the concepts required to solve addition and subtraction problems with large numbers. Casino games are usually designed to have a small negative expected value for the player, leading to a small positive. And Even MORE Practice with Scientific Notation (Boy, are you going to be good at this!) Positively positives! 41) What is the number of your street address in scientific notation?. In writing large numbers, American English uses a comma ( ,). com? Large-type. Clue: Large number. Numbers 12 - 19 are the same as 2-9 except with the number ten , สิบ ( sìp), in front of them. Every time you click the New Worksheet button, you will get a brand new printable PDF worksheet on Large Numbers. A wide variety of large numbers crop up in mathematics. 삼천구백오십오 억 = 3955억 or 3955,0000,0000 육십구 만 = 69만 or 69,0000 삼천오백육십팔 = 3568 Then. Number 1 Worksheets : Tracing, Coloring number 1 worksheets for preschool and kindergarten. Hi, I have working on a system in which I have to manipulate *very* big numbers. To achieve this we are using a data type (combination of data type and qualifiers) unsigned long long int to declare variable, read value and print. Large Numbers - Place Value, Number Name, Addition, Subtraction. If you're interested in the subject, but you don't know where to start, try reading about some basic functions and ideas:. Big Numbers Lyrics: Big numbers, big numbers / , that's a big number / Big numbers, big numbers / Whole team count it, that's a big number / Foreign cars, foreign broads / Foreign seats with the. Recommended Videos. Law of Large Numbers. Given two numbers as strings. The common usage of large numbers is spotted in monetary transactions and simple counting. Big Numbers. Since excel is the default for such files, it would "do its damage" before you get the file. Find the solution to 5000!, or explore hundreds of other calculators addressing math, finance, fitness, health, and more. How should we read numbers like these? How can we make it easier to read and write such large numbers?. 3 times 2 = 2+2+2. Related lesson plans: Class Number Book Students will practice counting to ten and one to one association. Every time you click the New Worksheet button, you will get a brand new printable PDF worksheet on Large Numbers. We cannot live without big and ambitious economic models. ehsaltiora. Modern numbers are great, but they can be pricey. Rounding large numbers. (After your visit, close the MegaPenny Project window to return to Math Cats. Dice Game For Saying Big Numbers. 2 million pounds. Following code implements the logic so that carry does not get truncated. There's not even that many atoms in the observable universe (estimated to be around 10^80). Large numbers are represented in Crusaders by adding a suffix in a similar way that computer memory is measured, the difference is that computer memory works in multiples of 1024 bytes to make 1 kilobyte; 1024 kilobytes to make 1 megabyte and so on. Wooden letters are the perfect accent for your space. Play Large Numbers quizzes on Sporcle, the world's largest quiz community. Multiplication of large numbers of n digits can be done in time O(nlog(n)) (instead of O(n 2) with the classic algorithm) thanks to the Fast Fourier Transform (FFT). The BigDecimal class represents a floating point value of arbitrary precision. This math worksheet gives your child practice subtracting 3-digit numbers. Read 73 reviews from the world's largest community for readers. My questions are: 1. Big O Tires, your auto service experts. Aurora Borealis February 18. Big Letter Event Hire - Unit 38 Abercorn Avenue, Hillington Industrial Estate,, G52 4JD Glasgow, United Kingdom - Rated 5 based on 100 Reviews "I. Numbers are separated into groups: ones, tens, hundreds, thousands, millions, and so on. In general, students have difficulty with two things when dealing with. Solid black numbers, print big numbers. This is a game for learning vocabulary words including zero, half, quarter, one thousand, one million, one billion. For seven, make a "peacock head" by putting all of your fingers on your thumb. Excel and really large numbers - they don't play nice together. We have already seen the numbers from 1 to 100 in Italian. Everyone has their own unique number sequence (in case you want to know yours), these numbers explain your life in terms of wealth,health and love. For example I have a factorial program that needs to save really huge integers that can be 50+ digits long. Numbers can be formatted to look like currency, percentages, times, or even plain old numbers with decimal places, thousands, and abbreviations. Hence the V at left has a line over the top, which means 5,000. The gmp package provides us a way of dealing with really large numbers in R. The integer primitive type with the largest range of value is the long, from -2 63 to 2 63 -1. Multiplication of Large numbers by 5 shortcut tricks are very important thing to know for your exams. You can choose to include answers and step-by-step solutions. For seven, make a "peacock head" by putting all of your fingers on your thumb. Large number is a crossword puzzle clue. The next step for your students is to practice until they become fluent and confident. 8 * 10^19 which. ” —Persi Diaconis and Frederick Mosteller, “Methods for Studying Coincidences” Earth is so heavy with people, my love, We’ve doubled our numbers since my arrival. Chords for The Big Numbers Song. For example, what is this number? 436,709,582,114. Mind you, these cannot give you a mathematical edge but they are fun to play and using my money management advice they might reduce the overall negative expectation of the game. English grammar tips with Gymglish, online English lessons. However, there is potential to engage children, as young as 10-12 years old, in investigations of. ‎Read reviews, compare customer ratings, see screenshots, and learn more about DragonBox Big Numbers. Bring a personalized touch to your home with the decorative wood letters and numbers from Michaels. For seven, make a "peacock head" by putting all of your fingers on your thumb. This page will show you how to pronounce a number. Like 'a lot of' and 'lots of', are 'a large number of' and 'large numbers of' used before uncountables as well as plurals?. As the number of experiments increases, the actual ratio of outcomes will converge on the theoretical, or expected, ratio of outcomes. Finally, Pickover has defined a superfactorial function, n$, defined as follows: n$ = n!n! n! | {z } n! copies and even 3$ has an enormous number of digits. We offer great quality at unbeatable prices. All numerical addition relies on the understanding that the sum does not change depending on the order in which the numbers are added, nor is the value of any number affected by breaking it into its component parts. If you stop to think a little you'll realize that this number is what creates all the other numbers in the world, whether it be above or below zero, and a decimal, fraction or whole number. The law of large numbers is one of the most important theorems in probability theory. Some Notes on Big Numbers. Check out our large house numbers selection for the very best in unique or custom, handmade pieces from our signs shops. You've been re-directed to the People Search on Yellow Pages, since Yellowpages. Big umbers (level: kids 7) for 9 or 10 years old children. Find a huge variety of in-stock designs of Letter Signs. List of prime numbers up to 1000 billion (12-digit number) If you find this site interesting, it has learned you 2-3 tips, may be it made you laugh or cry (uh?). Instead, it is the distance that light can travel in a year. It was cute. These assessments allow you to test your knowledge of different large. Description of the origin of the European number naming system. Numbers go on for ever, but our notation does not. How to put up a house number so people can see it. The human mind can barely comprehend a number that size you're literally 1 degree short of a googol. Practice big numbers by using different strategies from word to number, from number to words, or mutiple choice. Scotsbridge House, Scots Hill, Rickmansworth, WD3 3BB. Each number represents the following data structure: array of 1024 unsigned integer numbers (digits), the number of significant digits, the radix (from 2 to 36 inclusive) and the sign of this number (-1 or 1). About 25 percent of the students who attend the Little Rock School District's five high schools are absent today, according to Pamela Smith, communication's director for the district. Free Calendars! Need a calendar? Why spend money when you can get it for free? All of the calendars at Calendar Corner are free to download. when I run it for some smaller n it works fine but when I am trying to find some higher permutation such as last permutation i. The randomness comes from atmospheric noise, which for many purposes is better than the pseudo-random number algorithms typically used in computer programs. Large numbers are used mostly used in astronomy and cosmology. Sometimes a single number is the most important thing you want to track in your Power BI dashboard or report, such as total sales, market share year over year, or total opportunities. Japanese kids learn to multiply with a completely different method than the one kids in the US do. When the left brain was activated, they drew 6 to 12 bigger. Use this data type to efficiently calculate large numbers. Remove Ads. For example, the number 500 000 000 000 000 000 000 can be called 5 x 10 20 in scientific notation since there are 20 zeros behind the 5. Parents need to know that DragonBox Big Numbers is a resource-management game designed to give kids practice with multi-digit addition and subtraction, carrying and borrowing, and how to save up to meet your goals. The largest known prime has almost always been a Mersenne prime. How to name large numbers Suppose you want to know how to express 600 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 in words. Multiplication of Large numbers by 5 shortcut tricks are very important thing to know for your exams. We start with all numbers having a coat of adhesive that will stick to any smooth, clean surface. These basic Addition worksheets are made up of Horizontal Addition questions, where the math questions are written left to right. New to big numbers? Googology is the mathematical study of large numbers, their properties, and their nomenclature. What is large-type. Multiplying numbers together gives you a common multiple. Understanding concepts of big and small are important for math readiness. Practice big numbers and become champion of mathematics. The human mind can barely comprehend a number that size you're literally 1 degree short of a googol. Find clues for large number or most any crossword answer or clues for crossword answers. game and winning number updates sent to you. Example: 123456. Geometry Vocabulary. Super learning tool for schools. A numbers chart 1-20 is a very useful tool for teaching numbers to your child and practising one-to-one correspondence. Building address numbers are available in many type styles, colors and materials. My questions are: 1. Each category contains 4 digits, while each digit corresponds to a name. You are eligible for a full refund if no ShippingPass-eligible orders have been placed. For example, a random variable is repeatedly observed. 3 Names of Large Numbers. DLTK's Educational Activities Simple Number Templates. And it’s compatible with Apple Pencil. PROC SQL will not assign formats to derived variables. The length of 100 one dollar bills laid end-to-end measures 614 inches or 51. Synonyms for large number at Thesaurus. The largest known prime has almost always been a Mersenne prime. We can also refer to the number of digits for simple generalisations. - An infinite amount of additions and subtractions to solve. The human mind can barely comprehend a number that size you're literally 1 degree short of a googol. A large number phone or a big button phone can make using the telephone much easier. How big it can be - in binary presentation upto 2 ** 64 bits To speed it up it also has 2 ** 32 indexing version BigNumbers32. In English, numbers increase by thousands, so one thousand, one million, then one billion, a thousand times a million. Factorials reach astronomical levels rather quickly. Chords for The Big Numbers Song. Rounding Numbers Pirate Game. C/C++: Adding two big numbers. Customizable Large Numbers clocks from Zazzle. Choose your favourite or design your own from scratch!. Useful for elementary or pre-intermediate students to practice quickly and easily. 삼천구백오십오 억 천사백육십구 만 삼천오백육십팔 Break it down into pieces based on the 만/억/조. RISK AND UNCERTAINTY: A FALLACY OF LARGE NUMBERS' Erpcrienca shows that while R single cvcnt may have a probabilily alweed, D fawn. Binary Digits; Binary Number System; Binary Fingers; Hexadecimal. Multiplication is a basic arithmetic operation defined as the repetition of an addition. “This Easiphone has nice big numbers – ideal for the visually impaired – loads of space in the phone book for all those important numbers of relatives and friends and an emergency button on the rear of the phone which when pressed will run down a list of up to 5 contacts in turn until one of them answers the call. Standard calculators are limited with big numbers. Also known as the golden theorem, with a proof attributed to the 17th-century Swiss mathematician Jacob. com with free online thesaurus, antonyms, and definitions. Hey guys! Welcome to this video on subtracting large numbers. The randomness comes from atmospheric noise, which for many purposes is better than the pseudo-random number algorithms typically used in computer programs. Statistical estimation for Large Numbers of Rare Events. Multiplication of large numbers of n digits can be done in time O(nlog(n)) (instead of O(n 2) with the classic algorithm) thanks to the Fast Fourier Transform (FFT). Recommended Videos. Finally, Pickover has defined a superfactorial function, n$, defined as follows: n$ = n!n! n! | {z } n! copies and even 3$ has an enormous number of digits. Whoa! That's handy whenever you need to read something on your screen from further away—for example, phone numbers and passwords. -- Purdue University researcher Samuel Wagstaff is directing scientists around the world in a game of mathematical "Jeopardy," using powerful computers to divide and conquer numbers that have more than 100 digits. Affordable and search from millions of royalty free images, photos and vectors. English grammar tips with Gymglish, online English lessons. Big and small numbers are processed in different sides of the brain. This lesson plan for teachers of older teenage and adult students at low intermediate B1 level is about big numbers. Except, rather than deal with on-line delivery schedules, expense of sheet of cling material, and the stress of getting the numbers properly mounted on the sheet, I took the numbers and badge to a local sign company and had them match the font and color of the numbers and print them directly to the cling sheet. But a source.