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English Medium / Class 5 / Math / Number Work - Questions based on numbers from 1 to 100
Number Work - Questions based on numbers from 1 to 100
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Introduction

Number sense is the ability to understand the quantities and patterns of digits. In competitive exams, specific properties of numbers from 1 to 100 are often tested, such as digit frequency and common multiples.

Detailed Explanation of Digit Frequency

When we write numbers from 1 to 100, each digit (0-9) appears a specific number of times. Understanding this helps in solving complex logical problems.

DigitTotal Occurrences (1-100)Occurrences in 2-Digit NumbersTotal Numbers Containing the Digit
011910
1211920
2 to 9 (Each)201919
Table 2: Breakdown of Digit Occurrences from 1 to 100

Sub-topics

1. Double-Digit Identical Numbers

There are exactly 9 numbers between 1 and 100 where the units place and tens place digits are the same. These are all multiples of 11.

List: 11, 22, 33, 44, 55, 66, 77, 88, 99.

2. Multiples and Divisibility

Calculating how many times a number "fits" into 100 helps identify its multiples.

Examples

Example 1: Multiples of 8
Divide 100 by 8: 100 / 8 = 12.5.
There are 12 multiples of 8 below 100 (8, 16 ... 96).

Tricks and Shortcuts

  • The "One" Rule: Digit 1 is the most frequent digit (21 times) because it appears in the number 1, the entire 10-19 range, and the units place of 21, 31... up to 91, plus the 100.
  • Total Digits: To find total digits from 1-100: (9 numbers × 1 digit) + (90 numbers × 2 digits) + (1 number × 3 digits) = 9 + 180 + 3 = 192.

Common Mistakes

Students often miscount digit 0 as 10 times. Remember, 100 has TWO zeros, making the total count 11.

Practice Questions

Easy Questions

  1. How many times does the digit 7 appear in numbers from 1 to 100?
  2. List all multiples of 20 up to 100.
  3. What is the first two-digit number?

Medium Questions

  1. In the range 10-99, how many times does the digit 0 appear?
  2. How many numbers between 1 and 100 are multiples of both 3 and 5?
  3. How many times is digit 2 used at the tens place in numbers 1 to 100?

Hard Questions

  1. If you write all numbers from 1 to 100, which digits appear exactly 20 times?
  2. Calculate the total number of digits used to write numbers from 1 to 50.
  3. How many numbers between 1 and 100 have the digit 5 in either the units or tens place?

Revision Summary

Total digits used for 1-100 is 192. Digit 1 appears 21 times, 0 appears 11 times, and digits 2-9 appear 20 times each.

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