Decimals · Maths Practice

Key ideas

Multiplying decimals

1. Ignore the points and multiply.

2. Count the decimal places in the question.

3. Give the answer the same number of decimal places.

0.2 × 0.4: 2 × 4 = 8, two decimal places → 0.08

For harder ones, use a chimney sum, then count the decimal places.

Dividing by a decimal

Multiply both numbers by 10 (or 100) until the number you are dividing by is a whole number.

0.25 ÷ 0.5 → 2.5 ÷ 5

Then use a bus stop: 2.5 ÷ 5 = 0.5

Standard form, no calculator

Deal with the numbers and the powers of 10 separately.

Multiplying: add the powers. Dividing: take them away.

Check the number is still between 1 and 10.

Recurring decimals

Some fractions give decimals that repeat for ever.

13 = 0.333… = 0.3

211 = 0.1818… = 0.18

Dots go on the first and last digit of the repeating part.

Multiplying decimals

Decimals

Multiplying two decimals

Calculate 0.2 × 0.4.(2 marks)

Multiply the whole numbers.2 × 4 = 8✓¹

In plain EnglishIgnore the decimal points and multiply the non-zero digits: 2 × 4 = 8.

Count the decimal places.0.2 has 1, 0.4 has 1: 2 decimal places0.2 × 0.4 = 0.08✓²

In plain EnglishThere are 2 digits after the decimal points in the question, so the answer needs 2 decimal places. 8 becomes 0.08.

⚠ A common mistake: writing 0.8. Count the digits after the points in the question: there are two, so the answer has two.

Marking points

M1 2 × 4 = 8

M2 0.08

Decimals

A harder multiplication

Calculate 2.4 × 1.3.(2 marks)

Chimney sum.24 × 13

		1
		2	4
×		1	3
	1
		7	2
+	2	4	0
	3	1	2

24 × 13 = 312✓¹

In plain EnglishIgnore the points and multiply 24 by 13 with a chimney sum. 4 × 3 = 12: write 2 and carry the 1. 2 × 3 = 6, plus the carried 1 is 7, giving 72. Then 24 × 10 = 240. Add them: 312.

Count the decimal places.2.4 has 1, 1.3 has 1: 2 decimal places2.4 × 1.3 = 3.12✓²

In plain EnglishPut 2 decimal places back into 312. Check with an estimate: 2 × 1 = 2 and 3 × 1 = 3, so 3.12 is sensible.

Marking points

M1 312

M2 3.12

Dividing by a decimal

Decimals

Dividing by a decimal

Calculate 0.25 ÷ 0.5.(2 marks)

Make the number you divide by whole.0.25 ÷ 0.5= 2.5 ÷ 5 × 10 both numbers✓¹

In plain EnglishYou can't easily divide by 0.5, so multiply both numbers by 10. The answer stays the same.

Bus stop.

	0	.	5
5	2	.	²5

0.25 ÷ 0.5 = 0.5✓²

In plain English5 doesn't go into 2, so write 0 and carry the 2. Keep the decimal point in line. 25 ÷ 5 = 5.

⚠ Check: dividing by a number less than 1 makes the answer bigger than the number you started with: 0.5 > 0.25 ✓

Marking points

M1 2.5 ÷ 5

M2 0.5

Decimals

Multiplying by 100

Calculate 7.2 ÷ 0.08.(2 marks)

Make the number you divide by whole.7.2 ÷ 0.08= 720 ÷ 8 × 100 both numbers✓¹

In plain English0.08 has two decimal places, so multiply both numbers by 100. 0.08 becomes 8 and 7.2 becomes 720.

Bus stop.

		9	0
8	7	⁷2	0

7.2 ÷ 0.08 = 90✓²

In plain English8 doesn't go into 7, so carry the 7. 72 ÷ 8 = 9, and 0 ÷ 8 = 0.

Marking points

M1 720 ÷ 8

M2 90

Standard form without a calculator

Decimals

Multiplying in standard form

Without a calculator, find (3 × 10⁴) × (2 × 10⁵). Give your answer in standard form.(2 marks)

Multiply the numbers.3 × 2 = 6✓¹

In plain EnglishMultiply the front numbers together.

Multiply the powers of 10.10⁴ × 10⁵ = 10⁹ 4 + 5 = 9= 6 × 10⁹✓²

In plain English10⁴ has 4 zeros and 10⁵ has 5 zeros, so together that is 9 zeros: add the powers.

Marking points

M1 6

M2 10⁹

Decimals

When the number goes past 10

Without a calculator, find (5 × 10³) × (4 × 10²). Give your answer in standard form.(3 marks)

Numbers and powers.5 × 4 = 20✓¹10³ × 10² = 10⁵✓²

In plain EnglishMultiply the front numbers and add the powers.

Fix the front number.20 × 10⁵ = 2 × 10 × 10⁵= 2 × 10⁶✓³

In plain English20 is not between 1 and 10. 20 = 2 × 10, so the power goes up by one.

Marking points

M1 20

M2 10⁵

M3 2 × 10⁶

Decimals

Dividing in standard form

Without a calculator, find (8 × 10⁷) ÷ (2 × 10³).(2 marks)

Divide the numbers.82 = 4✓¹

In plain EnglishDeal with the number parts first: 8 divided by 2 is 4.

Divide the powers of 10.10⁷ ÷ 10³ = 10⁴ 7 − 3 = 4= 4 × 10⁴✓²

In plain EnglishDividing takes zeros away, so subtract the powers.

Marking points

M1 4

M2 10⁴

Recurring decimals

Decimals

A fraction as a recurring decimal

Write 56 as a recurring decimal.(2 marks)

Divide.5 ÷ 6 = 0.8333…✓¹

In plain EnglishDivide 5 by 6 (short division, or a calculator if allowed). The 3 keeps repeating for ever.

Use dot notation.56 = 0.83✓²

In plain EnglishOnly the 3 repeats, so it gets the dot. The 8 does not repeat.

Marking points

M1 0.8333…

M2 0.83̇

Decimals

A block that repeats

Write 311 as a recurring decimal.(1 mark)

Divide and look for the pattern.3 ÷ 11 = 0.272727…311 = 0.27✓¹

In plain EnglishThe block 27 repeats. Put a dot over the first and last digits of the repeating block.

Marking points

M1 0.27̇ with both dots

0 of 0 complete

Your turn

Non-calculator, apart from the 1/7 question. For standard form answers, type the number between 1 and 10 in the first box and the power in the second. Stuck? Tap Need a hint?