Decimals: tenths and hundredths
What the digits after the comma mean, how to compare, add, and multiply by 10 and 100. Read one step, play with it, then tap “I understand this”.
Tenths and hundredths
A decimal is a fraction with 10, 100 or 1 000 as denominator, just written differently. The comma separates the wholes from the parts: 0,47 = 47100.
The hundred square
The whole square is 1. Every column is a tenth; every small square is a hundredth.
In South Africa we write a decimal comma, not a point: 3,5 and not 3.5.
The comma shows where the wholes stop and the parts begin. Every place to the left is ten times bigger; every place to the right is ten times smaller. So after the ones come tenths, then hundredths.
Place value after the comma
| Tens | Ones | , | Tenths | Hundredths |
|---|---|---|---|---|
| 2 | 3 | , | 4 | 7 |
| 20 | 3 | 410 | 7100 |
23,47 = 20 + 3 + 0,4 + 0,07
Compare decimals
Give both numbers the same number of digits after the comma by adding zeros. 0,5 = 0,50, and that is bigger than 0,47.
Longer is not bigger! 0,47 has more digits than 0,5, but 0,5 is bigger.
Bigger or smaller?
Choose the right sign.
Correct: 00,5 is 5 tenths, which is the same as 50 hundredths. 50 hundredths is more than 47 hundredths. The first digit after the comma is worth the most.
Adding and subtracting: comma under comma
Write the numbers under each other with the commas lined up. Then add or subtract as with whole numbers, and put the comma straight down in the answer.
Comma under comma
Change the numbers and see how the commas stay in a line.
Just like ones under ones: tenths must be added to tenths and hundredths to hundredths. When the commas are under each other, every digit is in its right column.
Multiply and divide by 10, 100 and 1 000
Multiplying by 10 moves every digit one place to the left; dividing by 10 moves every digit one place to the right. With 100 they move two places.
Move the digits
Choose multiply or divide.
Every place is worth ten times more than the place to its right. Multiplying by 10 makes every digit worth ten times more, so every digit moves one place to the left. The comma itself stays put.
Fractions as decimals
| 12 | 510 | 0,5 |
| 14 | 25100 | 0,25 |
| 34 | 75100 | 0,75 |
| 15 | 210 | 0,2 |
| 110 | 110 | 0,1 |
Make the denominator 10 or 100 (equivalent fraction), then write the numerator after the comma.
Check yourself
- After the comma: tenths, hundredths, thousandths.
- Compare: give both the same number of digits after the comma (0,5 = 0,50).
- Adding and subtracting: comma under comma.
- × 10: digits move one place left. ÷ 10: one place right.
- Fraction to decimal: make the denominator 10 or 100.
Write these points in your maths book. Read them again the night before the test.
Quick questions
Tap an answer. If you get one wrong, read why and go back to that step. You get new questions every time.
You ticked all 6 steps! Now you are ready for the quiz.- Practice sheet for this classQuestions + memo · 2 A4 pagesPractice sheet
- Numbers16 pages · PDFPaperMemo
Ready for more? The Grade 6 decimals quiz gives you new questions every time.
- One step a day is enough. Ten calm minutes work better than an hour the night before the test.
- Money is decimal: R12,75 is 12 rand and 75 cents. Let your child compare and add prices at the shop.
- Ask your child to tell you the rule in their own words. If they can explain it, they understand it.
- The ticks (“I understand this”) are saved on this device only. We never ask for names or emails.
Follows CAPS for Grade 6 Maths. Always check your teacher’s notes and textbook too.