Lesson 6 of 8 · Grades 4 to 5
Rounding decimals
Rounding decimals uses the same rule as rounding whole numbers, only the neighbours change. The digit just to the right of the place you are rounding decides whether the number goes up or stays where it is.
The same rule, new neighbours
Rounding a decimal works exactly like rounding a whole number. The only change is the neighbours. To round 4.37 to the nearest tenth, the neighbours are 4.3 and 4.4. The number sits in that little gap, and you choose the nearer end.
The deciding digit for tenths
When you round to the nearest tenth, the deciding digit is the hundredths digit, one place to the right. For 4.37 the hundredths digit is 7, which is 5 or more, so the tenths digit grows from 3 to 4 and the answer is 4.4. For 4.32 the hundredths digit is 2, so the tenths digit stays at 3 and the answer is 4.3.
Round to the nearest whole number
To round to the nearest whole number, the deciding digit is the tenths digit. The number 4.62 sits between 4 and 5. The tenths digit is 6, which rounds up, so the answer is 5. The number 4.28 has a tenths digit of 2, so it rounds down to 4. The answer becomes a whole number, and the digits after the point are dropped.
Halfway again
The halfway rule is unchanged. The number 4.35 is exactly halfway between 4.3 and 4.4, so it rounds up to 4.4. The number 3.5 is exactly halfway between 3 and 4, so it rounds up to 4. When a decimal ends in a 5 in the deciding place, round up.
Watch out for this
Do not simply cross out the extra digits. Rounding 3.48 to the nearest tenth gives 3.5, not 3.4, because the hundredths digit 8 pushes the tenths digit up. Always look at the deciding digit before you write the answer, and be ready for a carry that changes the whole number: 12.95 to the nearest tenth is 13.0.
Where you meet it
Rounding decimals shows up in measurements. A pencil that measures 17.4 cm is about 17 cm long to the nearest whole centimetre. A bag that weighs 3.68 kg is about 3.7 kg to the nearest tenth. The measurement is close, the number is easier, and the unit does not change.
Worked example
Round 7.68 to the nearest whole number and to the nearest tenth.
Step 1: nearest whole number. The neighbours are 7 and 8. The tenths digit is 6, so round up to 8.
Step 2: nearest tenth. The neighbours are 7.6 and 7.7. The hundredths digit is 8, so round up to 7.7.
Step 3: check both answers on a number line. 7.68 sits between 7.6 and 7.7, nearer 7.7, and it is also nearer 8 than 7.
Step 4: the deciding digit for the whole number was the tenths digit 6; the deciding digit for the tenth was the hundredths digit 8.
Answer: 8 to the nearest whole number, and 7.7 to the nearest tenth.
Remember
- Rounding decimals uses the same rule as whole numbers.
- Nearest tenth: check the hundredths digit.
- Nearest whole number: check the tenths digit.
- 0 to 4 keeps the digit; 5 to 9 pushes it up.
Try it
Answer the five questions below. Work them out first, then open each answer to check.
-
Round 2.7 to the nearest whole number.
Show answer
3. The tenths digit is 7, so the number rounds up.
-
Round 1.34 to the nearest tenth.
Show answer
1.3. The hundredths digit is 4, so the tenths digit stays.
-
Round 5.86 to the nearest tenth.
Show answer
5.9. The hundredths digit is 6, so the tenths digit goes up.
-
Round 3.5 to the nearest whole number.
Show answer
4. It is exactly halfway, and the halfway rule sends it up.
-
A pencil is 17.4 cm long. What is that to the nearest whole centimetre?
Show answer
17 cm. The tenths digit is 4, so the ones digit stays.
Puzzle · Nearest tenth
Puzzle time
Which of these decimals rounds to 4.4 when rounded to the nearest tenth?
Show a hint
A number rounds to 4.4 when it is at least 4.35 and less than 4.45.
Show the answer
Answer: 4.42. 4.42 is between 4.35 and 4.45, so it rounds to 4.4. 4.34 rounds to 4.3, and 4.46 and 4.53 round to 4.5.