doing math

courses › Fractions, Decimals & Percents

Decimals

level 7 course

Line up, multiply, and divide decimals without losing the point.

Best in your head · no pen, no calculator why?

Learn first (about 3 minutes)

Opens at level 7.

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Builds on: Gaps & place value (not open yet)

the lesson

The idea, the techniques and a tip for each skill, right here. The Learn page adds worked examples for every skill and untimed practice.

Read the lesson · about 3 minutes

The idea

A decimal is a fraction with 10, 100 or 1,000 on the bottom: 0.3 is three tenths, and 0.25 is twenty-five hundredths. The decimal point marks where the whole numbers end.

Almost every decimal slip is a place-value slip. To add or subtract, line up the points so tenths meet tenths. To multiply or divide, work with whole numbers first, then put the point back where the size says it belongs. A rough estimate tells you whether the answer should be about 2, 20 or 200.

Techniques

Line up the points

Adding or subtracting decimals.

  1. Write the numbers with their decimal points lined up.
  2. Fill any gap with a zero, so 3.4 becomes 3.40.
  3. Add or subtract as if they were whole numbers, and keep the point in place.
worked example

Example: 6.3 − 2.45

  1. Line them up: 6.30 − 2.45.
  2. 630 − 245 = 385, so the answer is 3.85.

Answer: 3.85

Multiply, then place the point

Multiplying decimals.

  1. Leave out the points and multiply the whole numbers.
  2. Count the decimal places in the two numbers together.
  3. Give the answer that many decimal places, then drop any zeros at the end after the point.
worked example

Example: 0.75 × 8

  1. 75 × 8 = 600.
  2. 0.75 has two decimal places, so 6.00, which is 6.

Answer: 6

Clear the decimals, then divide

Dividing decimals.

  1. If the divisor, the number you divide by, has a point, multiply both numbers by 10.
  2. Repeat until the divisor is whole. The answer doesn't change, since both numbers grew by the same factor.
  3. Only the first number has a point? Divide as whole numbers, then give the answer that many decimal places.
  4. Check the size: dividing by a number below 1 gives a bigger answer.
worked example

Example: 4.8 ÷ 0.6

  1. Multiply both by 10: 48 ÷ 6.
  2. 48 ÷ 6 = 8.

Answer: 8

Tips by skill

  • TipAdd & subtract decimals: Line up the decimal points and fill gaps with zeros, so tenths add to tenths and hundredths to hundredths.
  • TipMultiply decimals: Multiply without the points, then give the answer as many decimal places as the two numbers have together.
  • TipDivide decimals: Multiply both numbers by 10 or 100 until the divisor is whole. If only the first has a point, divide, then put it back.

Watch out for

  • Lining up the last digits instead of the points. 3.4 + 2.15 is 5.55; treating 3.4 as 0.34 gives 2.49.
  • Forgetting to put the point back after multiplying. 2.5 × 8 is 20, not 200.
  • Placing the point by guesswork. 7.2 ÷ 0.9 is 8, not 0.8, because dividing by a number below 1 makes the answer bigger.

skills · practice stats

From rounds of this course only: box, review and test-out answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

  1. 1 day
  2. 3 days
  3. 7 days
  4. 14 days
  5. 30 days
  6. 60 days
  7. mastered · every 90 days

your rounds

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