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 NumberA number is a count or measurement that is really an idea in our minds. We write or talk about numbers using numerals such as "4" or "four". But we could also hold up 4 fingers, or tap the ground 4 times. These are all different ways of referring to the same number. There are also special numbers (like π (Pi)) that can't be written exactly, but are still numbers because we know the idea behind them. NumeralA numeral is a symbol or name that stands for a number. Examples: 3, 49 and twelve are all numerals. So the number is an idea, the numeral is how we write it. DigitA digit is a single symbol used to make numerals. 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are the ten digits we use in everyday numerals. Example: The numeral 153 is made up of 3 digits ("1", "5" and "3"). Example: The numeral 46 is made up of 2 digits ("4", and "6"). Example: The numeral 9 is made up of 1 digit ("9"). So a single digit can also be a numeral We can use other symbols too, for example hexadecimal also uses some letters! Digits -> Numerals -> NumbersSo digits make up numerals, and numerals stand for an idea of a number. Number Instead of NumeralBut often people (including myself) say "Number" when they really should say "Numeral" ... it doesn't really matter if you do that, because other people understand you. But try to use "digit" only when talking about the single symbols that make up numerals, OK? Other Types of Digits and NumeralsWe are all used to using numerals like "237" and "99", but the Romans used Roman Numerals, and there have been many other digits and numerals used throughout history. 10181, 10182, 10183, 10184, 10185, 10186, 10187, 10188, 10189, 10190 A number is basically a count or measurement. It is a mathematical value used for counting and measuring objects, and for performing arithmetic calculations. Numbers are broadly classified into the following categories,
Here, the categories in focus would be natural numbers and whole numbers. Natural Numbers All numbers ranging from 1 to infinite are referred to as natural numbers. Example: 1, 2, 10, 12 Whole numbers All-natural numbers along with the number 0 are referred to as whole numbers. Example: 0, 1, 2, 10, 12. Every natural number is a whole number but every whole number is not a natural number. Talking about digits, the numbers ranging from 0 to 9 are referred to as digits. Every number irrespective of its category is made up of digits. PermutationsA permutation is defined as the number of ways a particular set can be arranged, where the order of the arrangement matters. Order of arrangement means the order in which the elements are placed in the set. For example: [1, 2, 3] and [2, 1, 3] are two different permutations. Even though the elements are the same in both sets but their order of arrangement is different. Formula for Permutation
Formula is given above but the problems on permutations can easily be solved by logic. Solving through logic is better because the problem may be tricky and at times, the formula may confuse the student. How many different eight-digit numbers can be written using the digits 1, 2, 2, 3, 3, 4, 5?Solution:
Similar ProblemsQuestion 1: Given a set [1, 2, 3, 4, 5], generate all possible subsets of size 5. Solution:
Question 2: Given a set [1, 2, 3, 4, 5], generate all possible subsets of size 3. Solution:
Question 3: Generate all the different eight-digit numbers that can be written using the digits 1, 2, 3, 4, 5. Solution:
How many 3Hence, the required number of numbers =504.
How many different 4 digit numerals are there?There are 9000 four-digit numbers in all.
How many different six digit numbers are possible using the following numbers?Answer: There are 9,00,000 (nine lakh) 6-digit numbers in all.
How many combinations of numbers can you make with 10 digits?Hence, the 10-digit mobile number. This offers us 10 billion (1000 crore) different combinations, and as for the global population, it is highly unlikely to exceed this capacity.
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