top of page

1.2 Decimal Numbers

GCSE Maths Foundation · Edexcel · Chapter 1: Number

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: adding, subtracting, multiplying and dividing decimals, written methods and rounding to decimal places. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Add and subtract decimals by lining up the decimal points
  • Multiply and divide whole numbers and decimals by 10, 100 and 1000
  • Use written methods (grid, column and bus stop) to multiply and divide, including with decimals
  • Round numbers to a given number of decimal places

Key words

  • Decimal point: The dot that separates the whole-number part from the part smaller than 1.
  • Decimal place (d.p.): A position after the decimal point. 4.25 has 2 decimal places.
  • Tenth, hundredth: The first two columns after the point. 0.3 is 3 tenths, 0.07 is 7 hundredths.
  • Short division: The “bus stop” method for dividing by a single-digit number.

Adding and subtracting decimals

Write the numbers in columns so that the decimal points are lined up. Fill any gaps with zeros, then add or subtract as with whole numbers. The decimal point in the answer goes straight under the others.

Worked example: adding

Work out 14.6 + 3.75
Line up the points and write 14.6 as 14.60 so both numbers have 2 decimal places.
14.60 + 3.75 = 18.35

Answer: 18.35

Worked example: subtracting from a whole number

Work out 20 − 7.48
Write 20 as 20.00, then subtract: 20.00 − 7.48 = 12.52
Check: 12.52 + 7.48 = 20 ✓

Answer: 12.52

Multiplying and dividing by 10, 100 and 1000

Multiplying by 10, 100 or 1000 moves every digit 1, 2 or 3 places to the left. Dividing moves the digits to the right. The decimal point stays still.

Worked example: moving digits

(a) 4.7 × 100 = 470 (b) 0.085 × 1000 = 85
(c) 63 ÷ 100 = 0.63 (d) 42.7 ÷ 1000 = 0.0427

Answer: 470, 85, 0.63, 0.0427

Written methods for whole numbers

Grid method: split each number into parts (tens and units), multiply every pair, then add.

  • 30; 20 600; 6 180
  • 4; 20 80; 6 24

Worked example: grid method

Work out 34 × 26
600 + 180 + 80 + 24 = 884

Answer: 884

Bus stop (short division): divide into each digit from the left. Carry any remainder to the next digit.

Worked example: short division

Work out 924 ÷ 7
9 ÷ 7 = 1 remainder 2. Carry 2 to make 22.
22 ÷ 7 = 3 remainder 1. Carry 1 to make 14.
14 ÷ 7 = 2

Answer: 132

Multiplying and dividing decimals

Method: To multiply decimals: ignore the points, multiply the whole numbers, then give the answer the same total number of decimal places as the question. To divide by a decimal: multiply both numbers by 10 (or 100) until you are dividing by a whole number.

Worked example: multiplying

(a) 0.6 × 0.07: 6 × 7 = 42. There are 1 + 2 = 3 decimal places, so 0.042
(b) 3.4 × 2.6: 34 × 26 = 884. There are 2 decimal places, so 8.84

Answer: (a) 0.042 (b) 8.84

Worked example: dividing

Work out 7.56 ÷ 0.4
Multiply both by 10: 75.6 ÷ 4
Bus stop: 75.6 ÷ 4 = 18.9

Answer: 18.9

Rounding to decimal places

Count the decimal places you need, then look at the next digit. If it is 5 or more, round up. If it is 4 or less, keep the digit the same.

Worked example: rounding

(a) 12.3846 to 2 d.p.: the next digit is 4, so 12.38
(b) 0.0952 to 2 d.p.: the next digit is 5, so 0.09 rounds up to 0.10. Keep the final zero to show 2 d.p.

Answer: (a) 12.38 (b) 0.10

Common mistakes

  • Not lining up the decimal points when adding or subtracting. Write 14.6 as 14.60 so that tenths sit under tenths and hundredths under hundredths.
  • Writing 0.3 × 0.2 = 0.6. There are two decimal places in the question, so the answer is 0.06.
  • Dividing by a decimal without changing both numbers: 7.56 ÷ 0.4 is the same as 75.6 ÷ 4, not 7.56 ÷ 4.
  • Dropping a final zero when rounding: 0.0952 to 2 d.p. is 0.10, not 0.1.

Revision questions

Try these, then check your answers below each one.

Question 1. Work out 7.2 + 0.85.

Answer: 8.05

Working: 7.20 + 0.85 = 8.05.

Question 2. Work out 0.054 × 100.

Answer: 5.4

Working: 0.054 × 100 = 5.4.

Question 3. Work out 0.4 × 0.3. (Choose from: 0.12, 1.2, 0.012, 0.7.)

Answer: 0.12

Working: 4 × 3 = 12. There are 2 decimal places in the question, so 0.4 × 0.3 = 0.12.

Related lessons

Continue in the full course

This lesson is section 1.2 (EGCMF0102) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

bottom of page