Decimals Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Decimals.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Numbers written with a decimal point where each position to the right represents tenths, hundredths, thousandths, etc.

Money uses decimals: \$3.50 means 3 dollars and 50 cents (half a dollar).

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Decimals write parts of one using tenths, hundredths, thousandths, and so on.

Common stuck point: The procedure for decimals is the easy part; the trap is comparing decimals by digit count. Asking "What place value does each digit occupy?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: What place value does each digit occupy?

Worked Examples

Example 1

easy

Compute

3.75 + 2.48

Answer

6.23

First step

Align the decimal points and add column by column: ones, tenths, hundredths.

Full solution

2
Hundredths: $5 + 8 = 13$ , write 3 carry 1. Tenths: $7 + 4 + 1 = 12$ , write 2 carry 1. Ones: $3 + 2 + 1 = 6$ .
3
Result: $3.75 + 2.48 = 6.23$ .

When adding decimals, line up the decimal points so that digits with the same place value are in the same column, then add as with whole numbers.

Example 2

medium

Multiply

1.6 \times 0.35

Example 3

medium

Compute

4.5 \times 0.2

and explain the decimal placement.

Example 4

medium

Compute

12.4 \div 4

Example 5

hard

A board is

2.4

m long. It is cut into pieces of

0.3

m. How many pieces and how much is left?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

Subtract

8.03 - 2.57

Example 2

hard

Divide

7.2 \div 0.16

Example 3

easy

Write

\frac{3}{10}

as a decimal.

Example 4

easy

Write

0.07

as a fraction.

Example 5

easy

Compute

0.3 + 0.4

Example 6

easy

Compute

0.25 + 0.5

Example 7

easy

Compute

1.4 - 0.6

Example 8

easy

Which is bigger:

0.4

0.39

Example 9

easy

Round

3.47

to the nearest tenth.

Example 10

easy

Write

0.5

as a fraction in simplest form.

Example 11

medium

Compute

2.45 + 3.78

Example 12

medium

Compute

0.4 \times 0.6

Example 13

medium

Compute

7.2 \div 0.4

Example 14

medium

Write

\frac{3}{4}

as a decimal.

Example 15

medium

Compute

5 - 1.35

Example 16

medium

A jug holds

1.5

liters. How many full jugs from

10

liters of water? How much left over?

Example 17

medium

Order from smallest to largest:

0.5, 0.45, 0.405, 0.55

Example 18

medium

Compute

0.001 \times 1000

Example 19

medium

Write

0.\overline{3}

as a fraction. (Note: bar means repeating)

Example 20

challenge

Without a calculator, compute

1.5 \times 2.4

Example 21

challenge

Which is bigger:

\frac{2}{3}

0.67

Example 22

challenge

Express

0.\overline{142857}

as a fraction. (Hint: it's a well-known repeating decimal.)

Example 23

easy

Compute

0.9 - 0.4

Example 24

easy

Compute

0.2 + 0.7

Example 25

easy

Compute

1 - 0.6

Example 26

easy

Round

0.83

to the nearest tenth.

Example 27

easy

Compute

0.1 \times 10

Example 28

easy

Compute

0.5 \div 10

Example 29

medium

Compute

6.4 \div 0.8

Example 30

medium

Compute

2.5 + 0.75

Example 31

medium

Compute

9 - 0.8

Example 32

medium

A pencil costs

\$0.65

. How much do

8

pencils cost?

Example 33

medium

Compute

0.6 \times 0.5

Example 34

medium

Estimate:

4.9 \times 5.1

by rounding both factors.

Example 35

medium

Compute

0.25 \times 8

Example 36

hard

Compute

0.045 \times 200

Example 37

hard

Compute

3.6 \div 0.04

Example 38

hard

Compute

1.25 \times 0.8

Example 39

hard

Order from least to greatest:

0.305

0.35

0.3

0.3055

Example 40

hard

A water tank holds

12.5

L. After leaking at

0.25

L/h for

6

hours, how much remains?

Example 41

challenge

Without a calculator, compute

0.125 \times 0.8

Example 42

challenge

Show that

0.\overline{9}=1

by writing

x=0.\overline{9}

and solving for

x

← Back to Decimals Formula Explained Practice Mode

Related Concepts

Fractions Place Value Percentages Scientific Notation

Background Knowledge

These ideas may be useful before you work through the harder examples.

fractionsplace value