How to Compare Decimals? (+FREE Worksheet!)

Decimals are a way of displaying very small numbers without using a fraction. Decimal numbers are numbers that consist of two parts, integer, and decimal.

Fractions whose denominator is \(10\) or \(100\) or \(1000\) or … are called decimal fractions.

Note: In decimal numbers, the first digit after the decimal point is called the tenth, the second digit is the hundredth, the third digit is the thousandth, and so on.

Related Topics

• How to Add and Subtract Decimals
• How to Multiply and Divide Decimals
• How to Round Decimals

Step by step guide to compare decimals

A decimal is a fraction written in a special form. For example, instead of writing \(\frac{1}{2}\) you can write \(0.5\).
For comparing decimals:

• Step 1: First, compare the integers parts. In this case, the number is larger if the integer part is larger.
• Step 2: If the number of digits in the integer part of two decimal numbers were equal to each other, compare the digits in order from the left in such a way that first compare tenth, then hundredths, then thousandths, and so on. The first digit that was different indicates the larger and smaller number.
• Note: To compare numbers, use these symbols: Equal to \(=\), Less than \(<\), Greater than \(>\) Greater than or equal \(\geq\), Less than or equal \(\leq\)

Compare Decimals – Example 1:

Compare \(0.40\) and \(0.04\).

Solution:

\(0.40\) is greater than \(0.04\), because the tenth place of \(0.40\) is \(4\), but the tenth place of \(0.04\) is zero. Then: \(0.40 \ > \ 0.04 \)

Compare Decimals – Example 2:

Compare \(0.0912\) and \(0.912\).

Solution:

\(0.912\) is greater than \(0.0912\), because the tenth place of \(0.912\) is \(9\), but the tenth place of \(0.0912\) is zero. Then: \(0.0912 \ < \ 0.912 \)

Compare Decimals – Example 3:

Compare \(0.20\) and \(0.02\).

Solution:

\(0.20\) is greater than \(0.02\), because the tenth place of \(0.20\) is \(2\), but the tenth place of \(0.02\) is zero. Then: \(0.20>0.02 \)

Compare Decimals – Example 4:

Compare \(0.0210\) and \(0.110\).

Solution:

\(0.110\) is greater than \(0.0210\), because the tenth place of \(0.110\) is \(1\), but the tenth place of \(0.0210\) is zero. Then: \(0.0210<0.110\)

Exercises for comparing decimals

Write the correct comparison symbol (>, < or =).

1. \(\color{blue}{1.25 \ \ \ \ 2.3}\)
2. \(\color{blue}{0.5 \ \ \ \ 0.23}\)
3. \(\color{blue}{3.20 \ \ \ \ 3.2}\)
4. \(\color{blue}{4.58 \ \ \ \ 45.8}\)
5. \(\color{blue}{2.75 \ \ \ \ 0.275}\)
6. \(\color{blue}{5.2 \ \ \ \ 5}\)

Download Comparing Decimals Worksheet

1. \(\color{blue}{1.25 < 2.3}\)
2. \(\color{blue}{0.5 > 0.23}\)
3. \(\color{blue}{3.20  = 3.2}\)
4. \(\color{blue}{4.58 < 45.8}\)
5. \(\color{blue}{2.75 > 0.275}\)
6. \(\color{blue}{5.2 > 5}\)