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

## 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 =).

- \(\color{blue}{1.25 \ \ \ \ 2.3}\)
- \(\color{blue}{0.5 \ \ \ \ 0.23}\)
- \(\color{blue}{3.20 \ \ \ \ 3.2}\)
- \(\color{blue}{4.58 \ \ \ \ 45.8}\)
- \(\color{blue}{2.75 \ \ \ \ 0.275}\)
- \(\color{blue}{5.2 \ \ \ \ 5}\)

### Download Comparing Decimals Worksheet

- \(\color{blue}{1.25 < 2.3}\)
- \(\color{blue}{0.5 > 0.23}\)
- \(\color{blue}{3.20 = 3.2}\)
- \(\color{blue}{4.58 < 45.8}\)
- \(\color{blue}{2.75 > 0.275}\)
- \(\color{blue}{5.2 > 5}\)

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