Rounding

The objectives of this section are to

We round numbers when all we need is a reasonable approximation rather than the exact value.

The number 8.4236 can be rounded to a specified number of decimal places:

8.4236 → 8.424to 3 decimal places
8.4236 → 8.42 to 2 decimal places
8.4236 → 8.4 to 1 decimal places

The number 173.265 can be rounded to a specified number of significant figures:

173.265 → 173.27to 5 significant figures
173.265 → 173 to 2 significant figures
173.265 → 200 to 1 significant figure

A particular digit in a number will round up if the digit that follows it is 5, 6, 7, 8 or 9.

For example, 52.368 = 52.37 (to 2 decimal places).

The digit will remain unchanged if the following digit is 0, 1, 2, 3 or 4.

For example, 6.743 = 6.74 (to 3 significant figures).

1

Round 3647.5 to the nearest:

(a)

whole number,

Show
3648 Note that the 7 rounds up to 8, because it is followed by a 5.
(b)

ten (10),

Show
3650 Note that the 4 rounds up to a 5, because it is followed by a 7.
(c)

hundred (100),

Show
3600 Note that the 6 is unchanged, because the digit following it in the number is less than 5.
(d)

thousand (1000).

Show
4000 Note that the 3 rounds up to a 4, because it is followed by a 6.
2

Write 13.68952 correct to:

(a)

1 decimal place,

Show
13.7 to 1 decimal place.
(b)

3 decimal places,

Show
13.690 to 3 decimal places.
(c)

2 decimal places.

Show
13.69 to 2 decimal places.
3

Write:

(a)

3.642 correct to 2 significant figures

Show

3.6 correct to 2 significant figures.
(b)

314 269 correct to 3 significant figures,

Show

314 000 correct to 3 significant figures.

(Note the need for zeros to replace the remaining digits of the original number, to give a rounded number of comparable size.)
(c)

0.00723 correct to 1 significant figure.

Show

0.007 to 1 significant figure.

(Note that the zeros before the 7 are not significant, so they are not counted. The 7 is the first significant figure, i.e. it is the first digit that really determines the size of the number.)

Round each of the numbers below to the nearest whole number:

(a)
4.3
(b)
2.04
(c)
16.9
(d)
3.5
(e)
33.49
(f)
18.65

Round each of these numbers to the nearest ten:

(a)
187
(b)
309
(c)
8
(d)
35
(e)
44.9
(f)
16.4

The attendance at a football match was 36 475 people.

Round this number to:

(a)
the nearest 1000
(b)
the nearest 100
(c)
the nearest 10.

Write each of these numbers correct to 2 decimal places:

(a)
4.263
(b)
0.0472
(c)
10.8374
(d)
82.062
(e)
3.445
(f)
9.395

Write each of these numbers correct to 2 significant figures:

(a)
1.473
(b)
6.254
(c)
3.216
(d)
10.68
(e)
142
(f)
1374

Write the number 8.645712 correct to:

(a)
3 decimal places
(b)
4 decimal places
(c)
1 decimal place.

Write the number 147.52 correct to:

(a)
4 significant figures,
(b)
3 significant figures,
(c)
2 significant figures,
(d)
1 significant figure.

Write the number 104.735 correct to:

(a)
the nearest whole number,
(b)
2 decimal places,
(c)
2 significant figures,
(d)
1 decimal place,
(e)
1 significant figure.

Write each of the numbers below correct to 3 significant figures:

(a)
18.47
(b)
0.003265
(c)
147300
(d)
62.999
(e)
0.036247
(f)
0.00036945

A student completes the table opposite, but puts the accuracy statements against the wrong numbers.

Copy the table and put the statements against the numbers so that every pairing is correct.

0.047

0.003

16.22

184 200

7.06