# Comparing Decimals

Comparing decimals helps us to determine whether one or more decimals are smaller or larger in terms of their respective numeric values. We will put inequality symbols ‘<’ (lesser than) or ‘>’ (greater than) while comparing and ordering decimals.

Let us consider 2 decimals; 0.3 and 0.6.

Let us convert them to fractions considering the base as 10.

0.3 = 3/10, and 0.6 = 6/10

Since the denominators of both the fractions are same, we can easily compare the numerators.

3 < 6.

So 0.3 < 0.6

We will compare 0.64 and 0.68 with the help of models.

In the diagram above, we can see that 0.64 has fewer hundredths shaded as compared to 0.68.

So 0.64 < 0.68 or 0.68 > 0.64

We might be given to compare decimals with varying decimal places.

1. Line up the given numbers in the place value chart.
2. Compare the digits starting from the left with the greatest place value.
3. Keep comparing each digit in the place values till there is an inequality.
4. Show the relationship between the numbers with an inequality symbol (<, >, or =).

Since there is no digit in the 1000ths place in 0.72, we will annex a zero and write the 2 decimals in place value chart.

So, considering 0.842, the greatest place value is at the 10ths position. Its 8

Now considering 0.72, where the greatest place value is at the 10ths position. i.e., 7

Since 7 < 8, so, 0.72 < 0.842

Let us try comparing 0.534 and 0.5365

Writing the 2 decimals in place value chart and annexing zero as needed.

In 0.534 and 0.5365, the digits are same till the hundredth place. However, the digits at the thousandths place are different.

Since 4 < 6,

0.534 < 0.5365

We don’t need to annex the zeros. We can simply imagine the vacant places as no value.

When given more than two decimals, we compare and also order them using the inequality symbols.

## Comparing and Ordering Decimals

Let us try comparing and ordering 0.72, 0.07, and 0.7,

The digits at the ones place are the same.

Comparing the 10ths digits.

0 < 7,

So, 0.07  is the least among all three

Comparing the 100ths digits. Please note that 0.7 = 0.70

0 < 1,

So, 0.7 < 0.72

Ordering from least to greatest: 0.07, 0.7, 0.725

Ordering from greatest to least: 0.72, 0.7, 0.07

Better way to write:

0.07 < 0.7 < 0.72

Or

0.72 > 0.7 > 0.07

## Solved Examples

Compare 43.5 and 43.12

Solution:

Writing the decimals in place value chart as shown in the figure alongside.
5 > 1
∴ 43.5 > 43.12

Compare and order the following from greatest to least:

Solution:

Writing the decimals in place value chart as shown in the figure alongside.
9.34
83.9
21.4
0.96
Compare starting from the greatest place value.
Order:   83.9 > 21.4 > 9.34 > 0.96