Grade 6 Math · Topic 23

Converting Fractions to Decimals

Every fraction can be written as a decimal. The recipe: divide the numerator by the denominator. Many fractions give a clean terminating decimal; others give a repeating decimal pattern (use a bar over the repeating digits).

Lesson alignment: Prerequisite review · 5.NF.B.3 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Turn a fraction into a decimal

Divide the numerator by the denominator. The fraction bar and number line show the same amount.

Think first: For 5/16, about where should the decimal land between 0 and 1? What division could verify it?

Ready? Reveal the model and try your prediction

Swipe horizontally to see the full diagram.

Turn on JavaScript to adjust this model. The examples and practice below work without it.

Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

Convert 5/8 to a decimal.

Divide 5 ÷ 8. 5.000 ÷ 8 = 0.625 (terminating).

Answer: 0.625

Worked example 2

Convert 2/3 to a decimal.

Start by writing the calculation clearly: 2 ÷ 3 = 0.666… = 0.6̅ (repeating).

Answer: 0.6̅

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. 1/2 =
    Check

    0.5

  2. 3/4 =
    Check

    0.75

  3. 1/5 =
    Check

    0.2

  4. 7/8 =
    Check

    0.875

  5. 2/5 =
    Check

    0.4

  6. 9/10 =
    Check

    0.9

  7. 1/3 =
    Check

    0.3̅

  8. 5/6 =
    Check

    0.83̅

Try this situation 1

A pencil is 3/8 inch thick. Write its thickness as a decimal.

Show a worked solution

Answer: 0.375 inch.

Start by writing the calculation clearly: 3 ÷ 8 = 0.375 (terminating).

Try this situation 2

Mia answered 17/20 of the test questions correctly. Write her score as a decimal.

Show a worked solution

Answer: 0.85.

Start by writing the calculation clearly: 17 ÷ 20 = 0.85. Or equivalently 17/20 = 85/100 = 0.85.

Fresh questions · saved on this device

Practice this skill

12 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

Choose a session length

Your practice results stay in this browser and appear in the course progress report.

Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. A tailor uses 5/16 yard of ribbon for each hair bow. Which decimal represents this length?

2. During a science experiment, a beaker is filled with water to 3/5 of its total capacity. Which decimal correctly represents this portion of the beaker that is filled?

3. A coin is 1/4 inch thick. What decimal is equivalent to this thickness?

4. A recipe calls for 3/4 cup of sugar. Which decimal represents this amount?

5. Maria completed 11/20 of her homework. Which decimal represents the portion of homework she completed?

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

Your checkmark, skill-practice sessions, and best exit-check score are saved on this browser and device. The course page can download a progress report to share with a tutor or teacher.

More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Fractions & Decimals quiz ↗Try a full practice test ↗