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:
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.
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:
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.
