Place value and rounding
Rounding
One rule handles every degree of accuracy: look at the digit to the right, and let it decide.
The rule
When you round, you are told how accurate the answer should be. That is the DEGREE OF ACCURACY. For any degree of accuracy the method is the same: 1. Find the digit in the position you are rounding to. 2. Look at the digit to its RIGHT. 3. If that digit is 5 or more, increase your digit by 1. 4. If it is less than 5, leave your digit alone.
Worked example
Round 5.376398: To 1 d.p. — the first decimal digit is 3, and to its right is 7. Since 7 ≥ 5, round the 3 up to 4. Answer: 5.4 To 3 d.p. — the third decimal digit is 6, and to its right is 3. Since 3 < 5, leave the 6 alone. Answer: 5.376 To 5 d.p. — the fifth decimal digit is 9, and to its right is 8. Since 8 ≥ 5, round the 9 up. That carries: the 39 becomes 40. Answer: 5.37640
Keep the zeros
Rounding 34.8972 to 2 d.p. gives 34.90 — NOT 34.9. Both are the same value, but if you were asked for two decimal places, your answer must SHOW two decimal places. Writing 34.9 has only one, so it does not answer the question. The same applies to 5.37640: that final zero must be written, because five decimal places were asked for.
Worked examples
Round 5.376398 to 1 d.p.
- The first decimal digit is 3.
- The digit to its right is 7, which is 5 or more.
- So round the 3 up to 4.
Answer: 5.4
Round 5.376398 to 3 d.p.
- The third decimal digit is 6.
- To its right is 3, which is less than 5.
- So leave the 6 alone.
Answer: 5.376
Round 5.376398 to 5 d.p.
- The fifth decimal digit is 9.
- To its right is 8, so round up.
- The 39 carries to 40.
Answer: 5.37640
Round 34.8972 to 2 d.p.
- The second decimal digit is 9, and to its right is 7.
- Rounding up carries: 89 becomes 90.
Answer: 34.90 — the zero must be written
Why 34.9 is not the answer to 2 d.p.
- It is the same value as 34.90.
- But it shows only ONE decimal place.
Answer: It does not answer the question asked
Round 7.249 to 1 d.p.
- The first decimal digit is 2.
- To its right is 4, which is less than 5.
Answer: 7.2
Where you see this in real life
- Money is nearly always rounded to 2 d.p., which is why a till shows £3.40 rather than £3.4.
- A pedometer rounding your walk to 1 d.p. shows 4.0 km, not 4 km — the zero tells you how accurately it was measured.
Key words
- Round
- give a number to a stated accuracy
- Degree of accuracy
- how precise the answer must be
- Decimal place (d.p.)
- a position after the decimal point
- Decimal
- a number written with a decimal point
- Accuracy
- how precisely a value is given