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# Comparing Decimals

Sometimes, it is tricky to compare decimal numbers. We may reach at a wrong result, if we compare decimals by just having a look at them. We need to keep few things in our mind, while making comparison of decimal numbers.

• At first, compare the integer part i.e. whole number which is written before decimal point. If the integer part of a decimal number is bigger than that of the other, then that decimal number will definitely be greater than other one.
• When integer or whole number is equal in both numbers, we need to start comparing from left to right after decimal.
• Compare first digits (tenths) of both numbers after decimal. The decimal number which has bigger tenth digit is bigger.
• In case, if the tenth place digits in both numbers are equal, then compare next corresponding digits (hundredths). Continue comparing until we get the bigger digit in any number. The number with bigger digit after decimal point will be the bigger decimal number.
Let us take a look at few examples of comparing decimals.

Example 1:

Which one is greater: 0.34 or 0.320?

Solution:

 Ones (Integer) Decimal Tenth Hundredth Thousandth 0 . 3 4 0 0 . 3 2 0

Integral part of both numbers is equal. So, we shall compare numbers after decimal points.
Digit at tenth place in both numbers is 3. So, compare hundredth digits which are 4 and 2.
Since $4 > 2$. hence $0.34 > 0.320$.

Example 2:

Compare 5.671 and 5.67.

Solution:

 Ones (Integer) Decimal Tenth Hundredth Thousandth 5 . 6 7 1 5 . 6 7 0

Both the numbers have equal integers 5.
Here, corresponding tenth place digits are 6.
Corresponding hundredth place digits are 7.
Corresponding thousandth place digits are 1 and 0 respectively.
Since $1 > 0$
Hence $5.671 > 5.67$

Example 3:

Compare 6.34, 6.36, 5.31 and 6.51.

Solution:

 Ones (Integer) Decimal Tenth Hundredth 6 . 3 4 6 . 3 6 5 . 3 1 6 . 5 1

First, compare whole numbers. 5.31 is the smallest of all. This is because, it has the least whole number 5.
Compare digits at tenths place. 6.34 and 6.36 have the same tenths place digit.
Compare the hundredths places in 6.34 and 6.36.
We have $4 < 6$
So, $6.34 < 6.36$.

Therefore, we obtain the following order:
$5.31 < 6.34 < 6.36 < 6.51$

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