Get a complete idea of the concept of Comparing Decimal Fractions by going through the entire article. Learn what is meant by comparison of decimal fractions, How to Compare Decimal Fractions. Check out Solved Examples on Comparing Decimals explained step by step for better understanding. Apply the related knowledge to the problems you come across and solve them easily.
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Comparing Decimal Fractions – Definition
In a comparison of decimal fractions, we know that a decimal number has two parts i.e whole number part and decimal part. Comparison of decimals are notated as >, =, and <
- > used as a sign to indicate a greater number.
- < used as a sign to indicate a lesser number.
- = used as a sign to indicate that both are equal numbers.
How to Compare Decimal Fractions?
Go through the simple steps listed below for Comparing Decimal Fractions. They are in the below fashion
- First, check the whole number part of the given decimal numbers, assign the sign accordingly.
- If both given decimal numbers have the same whole number part, then compare the digits in the decimal part.
- If the tens digit in decimal place is also the same, then go for the hundreds digit and compare the numbers.
- If the digits in hundreds place are also the same, then compare the digits in further place and assign the sign.
Note: To make comparison easy, first convert the given decimals to like decimals and compare the numbers.
Comparing Decimals Examples
Example 1:
Compare 0.5 and 1.8?
Solution:
Given numbers are 0.5 and 1.8
Compare the whole number part of given decimal numbers that is
0 < 1
So, Now 1.8 is greater than 0.5.
Example 2.
Compare 0.4 and 0.8
Solution:
Given numbers are 0.4 and 0.8
Compare the whole number part of given decimal numbers that is
0 = 0
Now compare the digits in decimal part, a digit in tens place that is
4 < 8
So, Now 0.8 is greater than 0.4.
Example 3.
Compare 1.53 and 1.59
Solution:
Given numbers are 1.53 and 1.59
Compare the whole number part of given decimal numbers that is
1 = 1
Now compare the digits in decimal part, a digit in tens place that is
5 = 5
If the digit in tens place is equal then compare the next digit in hundreds place that is
3 < 9
So, Now 1.59 is greater than 1.53.
Example 4.
Compare 19.537 and 19.532?
Solution:
Given numbers are 19.537 and 19.532
Compare the whole number part of given decimal numbers that is
19 = 19
Now compare the digits in decimal part, a digit in tens place that is
5 = 5
If the digit in tens place is equal then compare the next digit in hundreds place that is
3 = 3
If the digit in hundreds place is equal then compare the next digit in thousands place that is
7 > 2
So, Now 19.537 is greater than 19.532.
Example 5.
Find which is greater in 209.116 and 209.118?
Solution:
Given numbers are 209.116 and 209.118
Compare the whole number part of given decimal numbers that is
209 = 209
Now compare the digits in decimal part, a digit in tens place that is
1 = 1
If the digit in tens place is equal then compare the next digit in hundreds place that is
1 = 1
If the digit in hundreds place is equal then compare the next digit in thousands place that is
8 > 6
So, Now 209.118 is greater than 209.116.
Example 6.
Find which is greater in 178.676 and 178.6
Solution:
Given numbers are 178.676 and 178.6
Compare the whole number part of given decimal numbers that is
178 = 178
Now compare the digits in decimal part, a digit in tens place that is
6 = 6
Now as the given numbers are not having equal decimal places so convert them into like decimals by adding zeros
we get 178.676 and 178.600
If the digit in tens place is equal then compare the next digit in hundreds place that is
7 > 0
So, Now 178.676 is greater than 178.600.
Example 7.
Write the following in ascending order
2.8, 2,801, 2.87, 2.81
Solution:
Given numbers
2.8, 2,801, 2.87, 2.81
To make comparison easy convert the given numbers into like decimals
Among the given numbers, the highest number of decimal places is 3, so add zeros accordingly
we get,
2.800, 2.801, 2.870, 2.810
By following steps rearrange them into ascending order
Now,
2.800 < 2.801 < 2.810 < 2.870.
Example 8.
Write the following in descending order
19.8, 19.01, 19.567, 19.2217
Solution:
Given numbers
19.8, 19.01, 19.567, 19.2217
To make comparison easy convert the given numbers into like decimals
Among the given numbers, the highest number of decimal places is 4, so add zeros accordingly
we get,
19.8000, 19.0100, 19.5670, 19.2217
By following steps rearrange them into descending order
Now,
19.8000 > 19.5670 > 19.2217 > 19.0100.