If you prefix the numbers with $0$s so that they are all three digits, you can ask the number of $2$s in the range $000$ to $999$. You should be able to convince yourself that the digits are equally distributed in this range. There are $3000$ digits, so $300\ 2$s. Deleting $000$ and adding $1000$ does not change the result. Show
Number Systems is a value used for counting and measuring objects, and for performing arithmetic calculations. It is a method of writing for expressing numbers. It provides a unique representation to every number and presents the arithmetic and algebraic form of the number. It enables us to operate arithmetic operations like addition, subtraction, multiplication, and division. An equation is a declaration that links two algebraic expressions of equal values with the ‘=’ sign. For example: In equation 8x + 4 = 7, 8x + 4 is the left-hand side expression and 7 is the right-hand side expression linked with ‘=’ sign. What is a Number?A word or symbol that indicates an amount is known as a number. The numbers 4, 6, 8, etc. are even numbers and 3, 5, 7, etc. are odd numbers. A number is a value formed by the combination of digits. These numbers are used to express algebraic quantities. An integer is an indication from a set of 10 characters ranging from 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Any amalgamation of integers represents a number. The size of a Number depends on the count of digits that are used for its development. For Example: 126, 128, 0.356, -12, 78, 94 etc. Whole Numbers Whole Numbers are the same as Natural Numbers, but they also include ‘zero’. We can donate whole numbers by the symbol W. Whole numbers include all the natural numbers and 0 (zero). We know that the numbers 1, 2, 3, 4, 5 are natural numbers. And the numbers 0, 1, 2, 3, 4, 5, 6 .. etc., are the whole numbers as they include 0 as well. Whole numbers are represented as W and Natural numbers are represented as N. Therefore, it is correct to say, W= {N} + 0 On the number line, everything which is on the right side of 0 (including 0) comes under whole numbers. How many times does the digit 1 appear in the numbers 1 to 1,000?Solution:
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