Decimals — Grade 8 Maths (CAPS)

What each digit after the decimal comma is worth, how to compare and order decimals correctly, and how to round off to a given number of decimal places — with a place-value chart, worked examples, a worksheet with memo and a quiz.

A decimal fraction is just another way of writing a fraction whose denominator is 10, 100, 1 000 and so on. Instead of writing 4/10 we write 0,4. Money, measurement and almost every calculator answer you will ever see is written this way, so place value has to be automatic.

1Place value after the comma

Each column to the right of the decimal comma is worth one tenth of the column before it.

In 32,475 the 4 is 4 tenths, the 7 is 7 hundredths and the 5 is 5 thousandths.

Worked ExampleWhat is the value of the 7 in 32,475?

1
Count the columns after the comma: 4 is tenths, 7 is hundredths.
First column = tenths, second = hundredths, third = thousandths.
2
So the 7 means 7 hundredths.
3
Value: 0,07, or 7/100.
Either form is accepted.

2Comparing and ordering decimals

Compare decimals column by column from the left — never by how many digits they have. A longer decimal is not automatically bigger.

Worked ExampleArrange in ascending order: 0,5, 0,45, 0,405, 0,54

1
Give them all the same number of decimal places: 0,500, 0,450, 0,405, 0,540.
Adding zeros at the end does not change a decimal's value.
2
Now compare as if they were whole numbers: 405, 450, 500, 540.
With equal decimal places the comparison is easy.
3
Ascending: 0,405, 0,45, 0,5, 0,54.
Write the answer using the original forms.

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Longer does not mean larger. 0,45 is smaller than 0,5, even though it has more digits — because 4 tenths is less than 5 tenths. Always compare the tenths column first.

3Rounding off

Look at the digit immediately after the place you are rounding to.
If it is 5 or more → round up. If it is 4 or less → leave the digit as it is.

Worked ExampleRound 3,678 to (a) two decimal places and (b) one decimal place

1
(a) Two decimal places means keep 3,67 and look at the next digit, 8.
The 8 is the deciding digit.
2
8 is 5 or more, so round the 7 up to 8 → 3,68.
3
(b) One decimal place means keep 3,6 and look at the next digit, 7.
Round the ORIGINAL number — do not use your answer from (a).
4
7 is 5 or more, so round the 6 up to 7 → 3,7.

⚠️

Never round twice. Rounding 3,649 to 2 dp gives 3,65, but rounding to 1 dp must go back to the original: 3,649 → 3,6 (not 3,7). Always round the original number in one step.

💡

In money questions, 'to the nearest cent' means 2 decimal places. So R14,678 becomes R14,68.

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Rounding can carry over. Rounding 9,996 to two decimal places gives 10,00: the 9 hundredths round up to 10 hundredths, which carries into the tenths and then the units.

4Multiplying and dividing by 10, 100 and 1 000

Multiplying by 10 moves every digit one place to the left — each digit becomes ten times as big. Dividing by 10 moves every digit one place to the right. For 100 move two places; for 1 000, three.

Worked ExampleCalculate (a) 3,47 × 100 and (b) 52,6 ÷ 1 000

1
(a) Two places to the left: 3,47 × 100 = 347.
Each digit is worth 100 times more.
2
(b) Three places to the right: 52,6 ÷ 1 000 = 0,0526.
Fill the empty places with zeros.

5Decimals and common fractions

Worked ExampleWrite 0,375 as a common fraction in its simplest form

1
Three decimal places means thousandths: 0,375 = 375/(1 000).
2
Divide the numerator and denominator by 125: 3/8.
125 is the highest common factor of 375 and 1 000.

Worked ExampleWrite 7/20 as a decimal

1
Make the denominator 100: 7/20 = 35/100.
Multiply the numerator and denominator by 5.
2
35/100 = 0,35.
35 hundredths.

Practice exercises

Work each one out, then click to reveal the answer.

📄 Worksheet ✅ Memo 📝 Exam paper 🗝️ Marking guide

1
What is the value of the 6 in 4,263?
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6 hundredths = 0,06
2
What is the value of the 9 in 0,915?
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9 tenths = 0,9
3
Write 7/100 as a decimal.
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0,07
4
Arrange in ascending order: 0,7, 0,65, 0,607, 0,76
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0,607, 0,65, 0,7, 0,76
5
Fill in < or >: 0,38 ___ 0,4
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0,38 < 0,4 (3 tenths is less than 4 tenths)
6
Round 5,472 to 2 decimal places.
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Next digit is 2 → 5,47
7
Round 5,472 to 1 decimal place.
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Next digit is 7 → 5,5
8
Round 12,996 to 2 decimal places.
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Next digit is 6 → 12,99 rounds up to 13,00
9
Round R23,4562 to the nearest cent.
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2 dp → R23,46