Fraction to Decimal Practice- Problems and Solutions

Why You Need to Master Fraction to Decimal Conversion

Most students stumble on this because their textbooks make it sound complicated. It isn't. Converting fractions to decimals is just division—nothing more. You'll encounter these problems in:

Middle school and high school math tests
College entrance exams
Everyday situations like cooking and measurements
Technical fields where precision matters

If you can't convert fractions to decimals quickly, you're wasting time on simple problems. That's embarrassing when you're taking a timed test.

The Basic Method: Divide the Numerator by the Denominator

This is it. The whole method. Take the top number, divide it by the bottom number, and you get your decimal. Example 1: Convert 3/4 to a decimal

3 ÷ 4 = 0.75

Done. No tricks.

Example 2: Convert 5/8 to a decimal

5 ÷ 8 = 0.625

Example 3: Convert 7/16 to a decimal

7 ÷ 16 = 0.4375

When the division doesn't end cleanly, you'll get a repeating decimal. Some fractions always produce these.

Common Fractions You Should Know Immediately

Memorize these. They're on every test:

Fraction	Decimal
1/2	0.5
1/4	0.25
3/4	0.75
1/3	0.333...
2/3	0.666...
1/8	0.125
3/8	0.375
5/8	0.625
7/8	0.875
1/5	0.2
1/10	0.1

Knowing these saves you calculation time. Tests don't give bonus points for showing your work on basic conversions.

Practice Problems with Solutions

Work through these. Check your answers only after you've tried.

Easy Level

Problem 1: Convert 1/4 to a decimal

Answer: 0.25

Problem 2: Convert 3/5 to a decimal

3 ÷ 5 = 0.6

Problem 3: Convert 9/10 to a decimal

9 ÷ 10 = 0.9

Problem 4: Convert 2/5 to a decimal

2 ÷ 5 = 0.4

Medium Level

Problem 5: Convert 7/8 to a decimal

7 ÷ 8 = 0.875

Problem 6: Convert 5/16 to a decimal

5 ÷ 16 = 0.3125

Problem 7: Convert 11/25 to a decimal

11 ÷ 25 = 0.44

Problem 8: Convert 9/20 to a decimal

9 ÷ 20 = 0.45

Harder Level

Problem 9: Convert 1/3 to a decimal

1 ÷ 3 = 0.333... (repeating)

The 3s go on forever. You can write this as 0.3̄ or 0.3̅

Problem 10: Convert 2/3 to a decimal

2 ÷ 3 = 0.666... (repeating)

Problem 11: Convert 1/7 to a decimal

1 ÷ 7 = 0.142857142857... (repeating cycle of 142857)

Problem 12: Convert 22/7 to a decimal

22 ÷ 7 = 3.142857... (this is the approximation for π)

How to Handle Repeating Decimals

When the division never ends with a remainder of zero, you get a repeating decimal. Here's how to spot them:

The remainder becomes 0 eventually → decimal terminates
The remainder never becomes 0 → decimal repeats
The repeating part can be 1 digit, 2 digits, or longer

Example: 1/11 = 0.090909...

The "09" repeats forever.

To write repeating decimals in standard form:

1/3 = 0.3̄ (bar over the 3)
2/11 = 0.1̄8 (bar over the 18)

Quick Method for Denominators of 10, 100, or 1000

When the denominator is a power of 10, conversion is instant. Example: 47/100

Just move the decimal two places left: 0.47

Example: 123/1000

Move decimal three places left: 0.123

Example: 5/100

Move decimal two places left: 0.05

Notice that 5/100 is the same as 1/20. Both equal 0.05.

Converting Mixed Numbers to Decimals

Mixed numbers have a whole number and a fraction. Example: 3 1/4

Step 1: Convert the fraction part: 1/4 = 0.25

Step 2: Add to the whole number: 3 + 0.25 = 3.25

Example: 5 3/8

3/8 = 0.375

5 + 0.375 = 5.375

Example: 2 5/16

5/16 = 0.3125

2 + 0.3125 = 2.3125

How to Check Your Answer

Multiply the decimal by the original denominator. You should get the numerator. Check: 3/8 = 0.375

0.375 × 8 = 3 ✓

Check: 7/20 = 0.35

0.35 × 20 = 7 ✓

This works every time. Use it when you're unsure.

Common Mistakes to Avoid

Forgetting to place the decimal correctly — Long division is where students lose marks. Don't rush it.
Confusing repeating decimals with approximations — 1/3 is exactly 0.333..., not approximately.
Dropping zeros when moving decimals — 0.05 is not the same as 0.5.
Not reducing fractions first — 2/4 reduces to 1/2, which is easier to convert.

Getting Started: Your Practice Routine

Set a timer for 10 minutes. Convert as many fractions as you can without looking at answers.

Start with denominators up to 12. When you're comfortable, move to denominators up to 20, then 50, then 100.

Every day, spend 5 minutes on 10 random conversions. After two weeks, you'll have these memorized.

The students who fail these problems are the ones who never practice. That's the only reason. Math skills are built through repetition, not through reading explanations.