Number and algebra · Lesson 1 of 4

Fractions, decimals and percentages

Three different ways of writing the same amount. Learn to switch between them quickly and the rest of the test gets easier.

About 20 min · Interactive · 8 practice questions

Drag the slider or pick a fraction. Every square is one hundredth of the whole grid, so the three readings always describe the same shaded area.

Fraction3/8
Decimal0.375
Percentage37.5%

One amount, three names

Most people treat fractions, decimals and percentages as three topics. They are one topic. Each is a way of saying "this much of a whole".

A fraction says it with two numbers: how many parts out of how many. A decimal says it using place value: tenths, hundredths, thousandths. A percentage is a decimal scaled to "out of 100", because 100 is easy to picture.

So converting never changes the amount. It only changes the label. The number line below shows the same points labelled all three ways.

Number line from 0 to 1 with benchmark fractions, decimals and percentages aligned fraction decimal percent 000% 1/80.12512.5% 1/50.220% 1/40.2525% 1/30.333…33.3% 2/50.440% 1/20.550% 3/50.660% 2/30.66766.7% 3/40.7575% 4/50.880% 7/80.87587.5% 11100%
Every point has three labels. Halfway is 1/2, 0.5 and 50% at the same time. Some fraction labels sit higher only so they don't overlap.

The six conversion methods

There are only six directions to convert in. Each one is a short, fixed recipe. Learn the recipe once and it works for every number.

Fraction to decimal

  1. If the bottom number fits into 10, 100 or 1000, scale top and bottom up to that.
  2. Otherwise divide the top by the bottom.

3/8 → ×125 → 375/1000 = 0.375

Decimal to percentage

  1. Multiply by 100.
  2. In practice: move the decimal point two places right.

0.375 → 37.5%

Percentage to decimal

  1. Divide by 100.
  2. In practice: move the decimal point two places left.

8% → 0.08 (not 0.8)

Decimal to fraction

  1. Count the decimal places. One place means tenths, two means hundredths, three means thousandths.
  2. Write the digits over 10, 100 or 1000.
  3. Simplify by dividing top and bottom by the same number.

0.45 → 45/100 → ÷5 → 9/20

Percentage to fraction

  1. Write the number over 100.
  2. Simplify.

35% → 35/100 → ÷5 → 7/20

Fraction to percentage

  1. If the bottom number fits into 100, scale to "out of 100" and read it off.
  2. Otherwise convert to a decimal first, then multiply by 100.

7/20 → ×5 → 35/100 = 35%

Why the scaling trick works

Multiplying the top and bottom of a fraction by the same number doesn't change its value. 3/8 and 375/1000 are the same amount, cut into smaller pieces. Once the bottom is 10, 100 or 1000, place value does the rest. This is the fastest method in the non-calculator section.

Conversion machine

Type any fraction, decimal or percentage

Try 3/8, 0.45, 12.5%, 1 1/4 or 2/3. The machine shows every step of the method, not just the answer.

    Benchmarks to know by heart

    The test assumes you know these without working. They are also your anchors for estimating: 0.68 is "a bit more than 2/3", which is often all a multiple-choice question needs.

    FractionDecimalPercentageHow to remember it
    1/20.550%Half
    1/40.2525%Half of a half; a quarter of a dollar is 25c
    3/40.7575%Three quarters of a dollar
    1/50.220%Each fifth is 0.2, so 3/5 = 0.6, 4/5 = 0.8
    1/100.110%Divide by 10
    1/80.12512.5%Half of 1/4; so 3/8 = 0.375, 5/8 = 0.625
    1/30.333…33⅓%Never stops: the 3 repeats forever
    2/30.666…66⅔%Double 1/3; rounds to 0.667
    1/200.055%Half of 10%
    1/1000.011%Divide by 100

    Hide a column, say each answer aloud, then click or tab to a striped cell and press Enter to check it.

    Comparing mixed forms

    Test questions often mix forms on purpose: "Which is largest: 5/8, 0.62, 61% or 3/5?" You cannot compare a fraction with a percentage by looking. You compare them after giving them the same name.

    Method for ordering

    1. Convert every value to a percentage (or every value to a decimal). Pick one form and stick to it.
    2. Write them in a column, lining up the decimal points.
    3. Compare digit by digit from the left.

    5/8 = 62.5%, 0.62 = 62%, 61% = 61%, 3/5 = 60%. Largest: 5/8.

    Pick the largest

    Four values, four different looks. Click the one you think is largest, then see them all on the same scale.

    Test scores as percentages

    A raw score like 18 out of 25 is a fraction in disguise: 18/25. Teachers convert scores constantly, and the test uses school contexts on purpose.

    General method

    1. Divide the score by the total.
    2. Multiply by 100.

    18 ÷ 25 = 0.72 → 72%

    Shortcut when the total fits into 100

    1. Find what turns the total into 100.
    2. Multiply the score by the same number.

    25 × 4 = 100, so 18 × 4 = 72 → 72%

    Score converter

      Common traps

      • Moving the point the wrong way. 8% is 0.08, not 0.8. Percentage to decimal makes the number smaller, so the point moves left.
      • Reading the decimal from the digits. 3/5 is not 0.35. The digits of a fraction do not become the digits of its decimal. Use a method.
      • Comparing by length. 0.62 is not bigger than 0.7 just because it has more digits. Line up the decimal points first.
      • Forgetting to simplify. 45/100 is correct but often not accepted when the question asks for "simplest form". Keep dividing until no common factor is left.
      • Treating 1/3 as 0.3. One third is 0.333…, which rounds to 33.3%. Using 0.3 makes every answer about 10% too small.
      • Percentage of what? "21 out of 28" means divide by 28, the total. Dividing by the wrong number is the most common error in score questions.

      ACER-style practice

      Eight questions in the formats the real test uses: multiple choice, type your answer, and true-or-false tables. Questions marked "no calculator" belong to the test's final section, where you cannot use one. Check each answer for a full explanation.

      0 of 8 checked

      What to remember

      • Fractions, decimals and percentages are three labels for the same amount.
      • Decimal to percentage: × 100. Percentage to decimal: ÷ 100.
      • Fraction to decimal: scale the bottom to 10, 100 or 1000, or divide top by bottom.
      • Decimal to fraction: write it over 10, 100 or 1000, then simplify.
      • To compare mixed forms, convert all of them to one form first.
      • Score as a percentage: score ÷ total × 100.

      All questions on this page are original and are not reproduced from ACER material. LANTITE is administered by the Australian Council for Educational Research.