# How to Compare Decimals? (+FREE Worksheet!)

Is it difficult for you to compare decimal numbers? In this blog post, you will learn more about decimal numbers and how to compare two decimal numbers. So join us!

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.

## 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. $$\color{blue}{5.2 \ \ \ \ 5}$$

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. $$\color{blue}{5.2 > 5}$$

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