Rounding and Conversion of Decimal Numbers
Primary 6 · Mathematics
Rounding and Conversion of Decimal Numbers
Lesson 3 of 5
35 min
Let's begin
Mutesi wants to share 10 000 Frw equally among 3 friends. Her calculator shows 3333.333333. But there is no such thing as a third of a franc! Knowing how to round long decimals helps you give sensible answers.
Rounding to the nearest thousandth (3 d.p.), ten-thousandth (4 d.p.), hundred-thousandth (5 d.p.) or millionth (6 d.p.) uses exactly the same steps: find the rounding place, look at the next digit, round up if it is 5 or more, then drop the rest.
| Round… | to the nearest… | Next digit | Answer |
|---|---|---|---|
| 0.4586 | thousandth | 6 → up | 0.459 |
| 2.718281 | ten-thousandth | 8 → up | 2.7183 |
| 2.718281 | hundred-thousandth | 1 → down | 2.71828 |
| 3.1415926 | millionth | 6 → up | 3.141593 |
Worked example 1
(a chain of 9s): Round 0.099996 to the nearest ten-thousandth.
Worked example 2
(money): Mutesi's 10 000 Frw ÷ 3 = 3333.333… Frw. Our smallest coin is 1 Frw, so we round down to whole francs: each friend gets 3 333 Frw, and 10 000 − 3 × 3 333 = 1 Frw is left over. (Rounding up to 3 334 Frw would need 10 002 Frw, which Mutesi does not have.)
Worked example 3
(an average): A cooperative weighs 7 bags of coffee: 24.8 kg, 25.6 kg, 25.1 kg, 26 kg, 25.3 kg, 25.9 kg, 25.3 kg. The total is 178 kg. The mean mass is 178 ÷ 7 = 25.4285714… kg. To the nearest hundredth, that is 25.43 kg.
Worked example 4
(a calculator): 1 ÷ 7 = 0.142857142… Rounded to the nearest millionth: 0.142857.
Worked example 5
(a measurement): A laboratory at a Rwandan university weighs a sample as 0.0036528 g. To the nearest hundred-thousandth, that is 0.00365 g.
Always think about the real situation: people, bottles and francs usually need whole numbers, while masses and lengths can keep decimals.
Tip
Put a line after the place you want. Write 0.0999|96 in your book. The digit just after the line decides whether you round up; everything after the line then disappears.
Work each one in your exercise book first, then tap Show answer to check.
Round 5.60729 to the nearest thousandth.
Answer: 5.607. The ten-thousandths digit is 2.
Round 0.1234567 to the nearest hundred-thousandth.
Answer: 0.12346. The millionths digit is 6.
Round 8.3999951 to the nearest millionth.
Answer: 8.399995. The seventh digit is 1, so round down.
Round 1.99996 to the nearest ten-thousandth.
Answer: 2.0000. The 9s all roll over.
2 000 Frw is shared equally among 6 pupils. How many whole francs does each get, and how many are left over?
Answer: 333 Frw each (2 000 ÷ 6 = 333.33…), with 2 Frw left over.
What you learned today
Sources and credits
The stories, Rwandan worked examples and practice questions were written by Ganzaa.
Quick check
Round 3.14159 to the nearest thousandth.
