Expressing Fractions as Decimals

Learn to convert fractions to decimals using three powerful methods!

1. Fractions with Denominator 10 or 100

The Easy Cases!

When the denominator is 10 or 100, conversion is super easy because tenths and hundredths are already places in a decimal!

Tenths (Denominator = 10)

Rule: $\frac{3}{10}$ is 3 tenths, so the numerator goes in the tenths place (the first digit after the decimal point). This works when the numerator is less than 10.

Ones	.	Tenths
0	.	3

$\frac{3}{10}$ = 0.3

$\frac{1}{10}$ = 0.1

$\frac{3}{10}$ = 0.3

$\frac{7}{10}$ = 0.7

$\frac{9}{10}$ = 0.9

Hundredths (Denominator = 100)

Rule: $\frac{14}{100}$ is 14 hundredths, so the numerator uses the tenths and hundredths places (two digits after the decimal point). This works when the numerator is less than 100.

Ones	.	Tenths	Hundredths
0	.	1	4

$\frac{14}{100}$ = 0.14

$\frac{14}{100}$ = 0.14

$\frac{26}{100}$ = 0.26

$\frac{3}{100}$ = 0.03

$\frac{7}{100}$ = 0.07

Watch out! For single-digit numerators, add a zero in the tenths place!

$\frac{3}{100}$ = 0.03 (not 0.3!)

2. Using Equivalent Fractions

The Strategy

If the denominator isn't 10 or 100, find an equivalent fraction that has 10 or 100 as the denominator!

Remember: Multiply both numerator and denominator by the same number.

Converting to Tenths

\frac{1}{2}

→(×5)

\frac{5}{10}

=0.5

2 × 5 = 10, so multiply top and bottom by 5

\frac{1}{5}

→(×2)

\frac{2}{10}

=0.2

5 × 2 = 10, so multiply top and bottom by 2

\frac{3}{5}

→(×2)

\frac{6}{10}

=0.6

Converting to Hundredths

\frac{1}{4}

→(×25)

\frac{25}{100}

=0.25

4 × 25 = 100, so multiply top and bottom by 25

\frac{3}{4}

→(×25)

\frac{75}{100}

=0.75

\frac{7}{20}

→(×5)

\frac{35}{100}

=0.35

20 × 5 = 100, so multiply top and bottom by 5

Common Fraction-Decimal Equivalents

Fraction	Equivalent	Decimal
$\frac{1}{2}$	$\frac{5}{10}$	0.5
$\frac{1}{4}$	$\frac{25}{100}$	0.25
$\frac{3}{4}$	$\frac{75}{100}$	0.75
$\frac{1}{5}$	$\frac{2}{10}$	0.2
$\frac{2}{5}$	$\frac{4}{10}$	0.4
$\frac{3}{5}$	$\frac{6}{10}$	0.6

3. Using Long Division

When to Use Long Division

Long division works for every fraction. It is most useful when you can't easily make an equivalent fraction with 10 or 100. Below, we use it first on two fractions whose answers you can check with equivalent fractions.

Remember: To change a fraction to a decimal, divide the numerator by the denominator.

Example: $\frac{3}{5}$ = 3 ÷ 5

5 cannot go into 3, so write 0 in the ones place and then the decimal point
3 ones = 30 tenths (write 3 as 3.0)
30 tenths ÷ 5 = 6 tenths
No remainder!

$\frac{3}{5}$ = 0.6

Example: $\frac{9}{4}$ = 9 ÷ 4

9 ÷ 4 = 2 remainder 1. Write 2 in the ones place, then the decimal point
Bring down 0: 10 tenths ÷ 4 = 2 tenths remainder 2 tenths
Bring down 0: 20 hundredths ÷ 4 = 5 hundredths
No remainder!

$\frac{9}{4}$ = 2.25

Alternative Method for $\frac{9}{4}$

You can also use equivalent fractions:

$\frac{9}{4}$ = 9 ÷ 4 = 2 + $\frac{1}{4}$ = 2 + $\frac{25}{100}$ = 2 + 0.25 = 2.25

4. Rounding Decimals

Recurring Decimals

Some fractions produce decimals that never end! We round these to the number of decimal places the question asks for. We do the same with a decimal that ends but has more places than the question asks for ( $\frac{7}{8}$ = 0.875 ≈ 0.88 to 2 decimal places).

Example: $\frac{5}{6}$ = 5 ÷ 6

The division keeps going! We get 0.8333... (3 repeats forever)

To 1 decimal place: $\frac{5}{6}$ ≈ 0.8

To 2 decimal places: $\frac{5}{6}$ ≈ 0.83

Rounding Rules

Look at the digit after the place you're rounding to:

• If it's 5 or more → round UP
• If it's less than 5 → round DOWN (keep the same)

Rounding to 1 decimal place

0.83... → Look at the 2nd digit after the decimal point: 3

3 < 5, so round down

Answer: 0.8

Rounding to 2 decimal places

0.833... → Look at the 3rd digit after the decimal point: 3

3 < 5, so round down

Answer: 0.83

More Rounding Examples

Fraction	Exact Decimal	1 d.p.	2 d.p.
$\frac{1}{3}$	0.333...	0.3	0.33
$\frac{2}{3}$	0.666...	0.7	0.67
$\frac{5}{6}$	0.833...	0.8	0.83
$\frac{1}{7}$	0.142857...	0.1	0.14

Note: Use ≈ (approximately equal) for rounded values

Practice Problems

Practice 1

Express $\frac{4}{5}$ as a decimal.

ShowHide solution

Method 1 (Equivalent fractions):
$\frac{4}{5}$ = $\frac{4 \times 2}{5 \times 2}$ = $\frac{8}{10}$ = 0.8

Method 2 (Long division):
5 cannot go into 4, so write 0 and the decimal point. 4 ones = 40 tenths, and 40 tenths ÷ 5 = 8 tenths. So 4 ÷ 5 = 0.8

Practice 2

Express $\frac{6}{8}$ as a decimal.

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Step 1: Simplify first: $\frac{6}{8}$ = $\frac{3}{4}$
Step 2: Convert: $\frac{3}{4}$ = $\frac{75}{100}$ = 0.75

Practice 3

Express $\frac{2}{3}$ as a decimal correct to 1 decimal place.

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2 ÷ 3 = 0.666...
Look at the 2nd digit after the decimal point (6): 6 is 5 or more, so round up
$\frac{2}{3}$ ≈ 0.7 (1 d.p.)

Practice 4

Express $\frac{17}{6}$ as a decimal correct to 2 decimal places.

ShowHide solution

Long division: 17 ÷ 6 = 2 remainder 5; 50 tenths ÷ 6 = 8 tenths remainder 2; 20 hundredths ÷ 6 = 3 hundredths remainder 2; 20 thousandths ÷ 6 = 3 thousandths remainder 2, and so on. So 17 ÷ 6 = 2.833...
Look at the 3rd digit after the decimal point (3): 3 < 5, so round down
$\frac{17}{6}$ ≈ 2.83 (2 d.p.)

Practice 5

Express 1 ÷ 4 as a decimal.

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1 ÷ 4 = $\frac{1}{4}$ = $\frac{25}{100}$ = 0.25

Key Takeaways

1.Fractions with denominator 10 (numerator less than 10): the numerator goes in the tenths place ( $\frac{3}{10}$ = 0.3)
2.Fractions with denominator 100 (numerator less than 100): the numerator uses 2 decimal places ( $\frac{14}{100}$ = 0.14)
3.Use equivalent fractions to convert to 10ths or 100ths when possible
4.Use long division when equivalent fractions don't work easily
5.Round to the decimal places asked for: look at the next digit; 5 or more rounds up, 4 or less rounds down
6.Use ≈ (approximately equal) for rounded values

Expressing Fractions as Decimals

1. Fractions with Denominator 10 or 100

The Easy Cases!

Tenths (Denominator = 10)

Hundredths (Denominator = 100)

2. Using Equivalent Fractions

The Strategy

Converting to Tenths

Converting to Hundredths

Common Fraction-Decimal Equivalents

3. Using Long Division

When to Use Long Division

Example: 35\frac{3}{5}53​ = 3 ÷ 5

Example: 94\frac{9}{4}49​ = 9 ÷ 4

Alternative Method for 94\frac{9}{4}49​

4. Rounding Decimals

Recurring Decimals

Example: 56\frac{5}{6}65​ = 5 ÷ 6

Rounding Rules

Rounding to 1 decimal place

Rounding to 2 decimal places

More Rounding Examples

Practice Problems

Practice 1

Practice 2

Practice 3

Practice 4

Practice 5

Key Takeaways

Example: $\frac{3}{5}$ = 3 ÷ 5

Example: $\frac{9}{4}$ = 9 ÷ 4

Alternative Method for $\frac{9}{4}$

Example: $\frac{5}{6}$ = 5 ÷ 6