Decimals and Fractions 3
Fractions and Decimals

Some fractions can be written as decimals with a fixed number of decimal places, for example:

= 0.25

These are called terminating decimals. Others have an infinite number of decimal places, for example:

= 0.333 333...

Numbers that contain an infinite number of decimal places are usually rounded to a specified number of significant figures or decimal places.

Remember that significant figures are counted from left to right, starting from the first non-zero digit; decimal places are counted after the decimal point.

Worked Examples

1

Round each number in the list below to:

(i) 3 significant figures (ii) 3 decimal places.
(a)

4 732.165

Show me
(i)

4 732.165 = 4 730 to 3 significant figures. Note that only the first 3 figures are considered.

(ii)

4 732.165 = 4 732.165 to 3 decimal places. There is no charge as there are exactly 3 figures behind the decimal point.
(b)

4.736 1

Show me
(i)

4.736 1 = 4.74 to 3 significant figures. The first three figures are considered and the 3 is rounded up to a 4, because it is followed by a 6.

(ii)

4.736 1 = 4.736 to 3 decimal places. The 6 is not rounded up because it is followed by a 1.
(c)

417.923 5

Show me
(i)

417.923 5 = 418 to 3 significant figures. The first 3 figures are used and the 7 is rounded up to 8 because it is followed by a 9.

(ii)

417.923 5 = 417.924 to 3 decimal places. There are three figures behind the decimal point and the 3 is rounded up to a 4 because it is followed by a 5.
(d)

0.056 234

Show me
(i)

0.056 234 = 0.056 2 to 3 significant figures. Note that the zeros at the start of this number are not counted.

(ii)

0.056 234 = 0.056 to 3 decimal places.
(e)

0.004 721

Show me
(i)

0.004 721 = 0.004 72 to 3 significant figures. Note that the zeros in front of the 4 are not counted.

(ii)

0.004 721 = 0.005 to 3 decimal places. The 4 is rounded up to a 5 because it is followed by a 7.
2

Convert each of the following fractions to decimals,

In each case the bottom number should be divided into the top number. This will require long division.

(a)

Show me

To convert , divide 4 into 1.

0.25
41.00
8
20
20
0

So = 0.25.
(b)

Show me

To convert , divide 3 into 2.

0.666. . .
32.000
18
20
18
2

So = 0.666 6. . . = 0.667 to 3 decimal places.
(c)

Show me

To convert , divide 5 into 4.

0.8
54.0
40
0

So is exactly 0.8.
(d)

Show me

To convert into a decimal, divide 7 into 3.

0.42857. . .
73.00000
28
20
14
60
56
40
35
50
49
1

There will be an infinite number of decimal places in this case, but

= 0.428 6

correct to 4 decimal places.

Exercises

Write each of the following numbers correct to:

(i) 2 significant figures (ii) 2 decimal places.
(a)
18.643(i)(ii)
(b)
1 024.837(i)(ii)
(c)
16.04(i)(ii)
(d)
181.435(i)(ii)
(e)
16.824(i)(ii)
(f)
0.083 741(i)(ii)
(g)
0.009 562(i)(ii)
(h)
4.837 5(i)(ii)
(i)
3.864 9(i)(ii)

Write the number 48 637.012 45 correct to

(a)
3 significant figures
(b)
2 decimal places
(c)
4 decimal places
(d)
4 significant figures
(e)
3 decimal places
(f)
2 significant figures.

Write each number correct to the number of decimal places or significant figures specified.

(a)
0.00472 (2 s.f.)
(b)
48.234 (3 s.f.)
(c)
15.83 (1 s.f.)
(d)
4.862 (2 d.p.)
(e)
18.415 (2 d.p.)
(f)
21.804 (2 d.p.)
(g)
14862 (2 s.f.)
(h)
0.00463 (3 d.p.)
(i)
0.004178 (3 s.f.)
(j)
15682 (3 s.f.)
(k)
54631 (2 s.f.)
(l)
31.432 (3 s.f.)
(m)
14.176 (4 s.f.)
(n)
0.815 (2 s.f.)
(o)
1.84149 (3 d.p.)
(p)
15.013 (3 s.f.)
(q)
14.1704 (3 d.p.)
(r)
201.04 (3 s.f.)

The number of spectators that enter a football ground for a big match is 44 851.

(a)

Write this number correct to 1, 2, 3 and 4 significant figures.

(1 s.f.) (2 s.f.) (3 s.f.) (4 s.f.)
(b)

How many significant figures in your answers to (a) makes the number of spectators appear

(i)
the largest
(ii)
the smallest?

Write each of the following fractions as a decimal correct to 4 decimal places.

(a)
(b)
(c)
(d)
(e)
(f)

(a)

Change to a decimal.

(b)

Write the letters of these numbers in order of size. Start with the smallest.

A: 0.805, B: 0.85, C: , D: 0.096