Comparing Numbers

Comparing numbers means looking at two or more numbers to see which is bigger, smaller, or if they are equal.

We use special symbols to compare numbers:

Example:

👁 school1

• In the first part, 8 is greater than 6 because there are more blocks.
• In the second part, 5 is equal to 5 because both sides have the same number of blocks.
• In the third part, 6 is less than 8 because there are fewer blocks.

Comparing Numbers Exercise

You can check your understanding of the concept in the following quiz:

Rules for Comparing Numbers

To compare number we can use the following 2 rules to compare numbers:

Rule 1: Number of Digits

When you're comparing two numbers, first count the digits in each number. A number with more digits is always greater because each additional digit increases its place value.

Examples:

345 > 89 (345 has 3 digits and 89 has 2 digits)

1000 > 999 (1000 has 4 digits and 999 has 3 digits)

Rule 2: Leftmost Digit

If two numbers have the same number of digits, compare their leftmost digits. The number with the greater leftmost digit is the greater number.

Example: 323 > 232 (Both have 3 digits, but 3 > 2)

Note: If the leftmost digits are the same, we move to the next digit to the right. This keeps going until we find digits that are different.

Example: 5678 > 5612 (Both have 4 digits. Leftmost digits 5 = 5, next digits 6 = 6, compare next: 7 > 1)

Comparing Numbers on a Number Line

Steps to compare numbers on a number line are:

Step 1: Draw a number line with positive and negative numbers, as well as zero.

Step 2: Locate the numbers you want to compare.

Step 3: Look at the positions of the numbers relative to each other on the line.

• The number to the right is greater.
• The number to the left is smaller.
• If both numbers are at the same position, they are equal.

Example: Compare the numbers -3 and 2 on a number line.

Solution:

👁 number

Since -3 is to the left of 2 on the number line, we can say that -3 is less than 2.

Comparing Integers

Integers are a set of numbers that include all whole numbers and their negatives. The set of integers is denoted by Z and includes ..., -3, -2, -1, 0, 1, 2, 3, ...

Example: Compare -57 and -173.

57 has 2 digits.

173 has 3 digits.

The number with more digits is greater.

173 > 57

When we multiply -1 both sides, comparison sign reverse.

Therefore, -173 < -57.

Comparing Rational Numbers

A rational number is a number that can be expressed in the form p/q, where p and q are integers and q ≠ 0. Rational numbers include all integers, fractions, and terminating or repeating decimals.

Example: Compare 3/5 and 4/7

L.C.M of 5 and 7 are 35.

3/5 = 21/35
4/7 = 20/35

Since, denominator of rational numbers are same, We can compare numerators.
= 21 > 20 (Comparing Numerators)
= 21/35 > 20/35

Therefore, 3/5 > 4/7

Comparing Decimals

Decimals are numbers that have a whole number part and a fractional part separated by a decimal point. For example, in the number 12.345, 12 is the whole number part, and 345 is the fractional part.

Example: Compare 0.256 and 0.259.

Compare digit by digit from left to right:

First digits: 0 = 0

Second digits: 2 = 2

Third digits: 5 = 5

Fourth digits: 6 < 9

So, 0.256 < 0.259.