�2 3.1 Conversion between fractions and decimals

77A

1 Write each of the following sets of numbers in order of size.

Start with the smallest number each time.

a 0.45, 0.6, 0.5, 0.4, 0.54 b 0.74, 0.4, 0.47, 0.7, 0.44

.............................................................................................. ..............................................................................................

c 0.8, 0.18, 0.88, 0.81, 0.08, 0.1 d 5.63, 5.6, 5.3, 5.06, 5.36

.............................................................................................. ..............................................................................................

e 7.9, 7.039, 7.39, 7.033, 7.93, 7.933

..............................................................................................

2 Write each of these decimals as fractions.

units tenths hundredths thousandths

a 0 . 0 1

b 0 . 0 0 9

c 0 . 5 3

d 4 . 7

e 5 . 0 8 3

3 Write each of these decimals as fractions.

a 0.7 ............................ b 0.09 ............................ c 0.003 ............................ d 0.13 ............................

e 3.1 ............................ f 0.029 ............................

4 Write each of these as fractions in their simplest form.

a 0.8 .................................................................................. b 0.36 ..................................................................................

c 0.006 ............................................................................. d 0.128 ...............................................................................

e 3.75 ............................................................................... f 8.02 ..................................................................................

g 23.025 ........................................................................... h 7.0056 .............................................................................

Guided practice worksheet

Write the numbers underneath each other, in the space below, with the decimal points lined up.

a ........................................................................

b ........................................................................

c ........................................................................

d ........................................................................

e ........................................................................

The place value of the last column each time gives you the denominator of the fraction.

Questions are targeted at the grades indicated

�2 3.1 Conversion between fractions and decimals

77B

Guided practice worksheet

5 Write each of these fractions as a decimal.

a 4

100 .................................................... b 65

100 .................................................... c 7

10 .........................................................

d 2

1000 ................................................... e 343

1000 .................................................. f 3

100000 ....................................................

6 Write each of these fractions as a decimal.

a 35 ....................................................... b

150 .................................................... c

320 ..........................................................

d 625 ...................................................... e

34 ....................................................... f

63250 .........................................................

g 14 ....................................................... h

950 ..................................................... i

12 ...........................................................

j 39

500 .................................................... k 101200 .................................................... l

3125 ........................................................

7 Write the following sets of numbers in order. Start with the smallest each time.

a 45, 0.45, 0.85, 1925, 0.78 b

14, 0.2,

310,

25, 0.35

....................................................................... .......................................................................

c 57100, 35, 0.58, 0.65,

1425 d

920, 0.43,

1125, 0.34, 0.4

....................................................................... .......................................................................

e 1725, 0.7, 35, 0.69,

1320

.......................................................................

To order a mixture of fractions and decimals, � rst change the fractions into decimals.

If the number on the bo� om of a fraction is 10, 100, 1000, etc then this tells you the number of decimal places in the decimal.

If the number on the bo� om of a fraction is not 10, 100, 1000. etc, then turn the fraction into an equivalent fraction with one of these numbers on the bo� om.

�2 3.2 Carrying out arithmetic using decimals

79A

1 Work out

a 5.46 + 6.39 b 23.1 + 5.43 c 46 + 4.35 + 0.8

............................................ ............................................ ............................................

d 74.35 – 8.62 e 78.9 – 6.37 f 9.83 – 2.347

............................................ ............................................ ............................................

2 Work out

a 34 × 1000 b 57.2 × 10 c 9.03 × 1000

............................................ ............................................ ............................................

d 0.045 × 100 e 0.621 × 1000 f 43.9 × 100

............................................ ............................................ ............................................

3 Work out

a 13 ÷ 10 b 420 ÷ 100 c 8 ÷ 100

............................................ ............................................ ............................................

d 12.6 ÷ 100 e 3.4 ÷ 100 f 23.52 ÷ 10

............................................ ............................................ ............................................

4 Work out

a 0.3 × 0.4 b 0.07 × 0.08 c 0.01 × 0.4

............................................ ............................................ ............................................

Guided practice worksheet

Count the total number of decimal places in the question; the answer must have the same number of decimal places.

Remember to line up the decimal points.

Questions are targeted at the grades indicated

�2 3.2 Carrying out arithmetic using decimals

79B

Guided practice worksheet

d 0.006 × 0.5 e 1.2 × 0.3 f 4.3 × 0.02

............................................ ............................................ ............................................

5 Work out

a 2.43 × 2.1 b 1.85 × 0.32 c 92.3 × 5.3

............................................ ............................................ ............................................

d 6.75 × 0.43 e 0.123 × 0.45 f 0.048 × 2.7

............................................ ............................................ ............................................

6 Work out

a 16 ÷ 0.2 b 15 ÷ 0.03 c 24 ÷ 0.4

............................................ ............................................ ............................................

d 48.2 ÷ 0.2 e 68.4 ÷ 0.04 f 3.75 ÷ 0.05

............................................ ............................................ ............................................

7 Work out

a 4.2 ÷ 0.3 b 0.145 ÷ 0.5 c 19.2 ÷ 0.03

............................................ ............................................ ............................................

d 0.048 ÷ 0.6 e 1.28 ÷ 0.004 f 0.805 ÷ 0.007

............................................ ............................................ ............................................

Multiply both numbers by a power of 10 so that the second number is no longer a decimal.

�2 3.3–3.4 Rounding, decimal places and signi� cant � gures

81

1 Write each of these numbers correct to 1 signi� cant � gure.

a 6.4 ...................................... b 3.8 ...................................... c 17.8 ......................................

d 378 ...................................... e 94.79 ......................................

2 Write each of these numbers correct to 1 signi� cant � gure.

a 0.64 ...................................... b 0.0038 ...................................... c 1.0038 ......................................

d 0.0099 ...................................... e 0.6009 ......................................

3 Write each of these numbers correct to 3 signi� cant � gures.

a 6.456 ...................................... b 3.142 ...................................... c 17.88 ......................................

d 37802 ...................................... e 94.01 ......................................

4 Write each of these numbers correct to 3 signi� cant � gures.

a 0.6411 ...................................... b 0.03088 ...................................... c 1.0038 ......................................

d 0.009999 ...................................... e 0.6009 ......................................

Do not forget that that there must be only one � gure in your answer that is not a zero.

Zeros in the middle of a number are signi� cant.

Don’t forget there is a di� erence between 6.0 (2 signi� cant � gures) and 6.00 (3 signi� cant � gures).

Any leading zeros are not signi� cant � gures, so think about the � rst non-zero � gure in each number.

Guided practice worksheet Questions are targeted at the grades indicated

�2 3.5 Estimating calculations by rounding

83A

1 Work out an estimate in each case by � rst rounding each number correct to 1 signi� cant � gure.

a The area of a rectangle 20.3 cm by 39.2 cm.

.......................................................................................................................................

b The area of a square with a side of length 51 cm.

.......................................................................................................................................

c The total length of 48 rods each of length 5.8 metres.

.......................................................................................................................................

2 Work out an estimate for the value of each of

a 17.8 × 31.1 b 99.8 × 41.2

.............................................................. ..............................................................

c 37.9 × 51.3 d 487 × 316

.............................................................. ..............................................................

3 Work out an estimate for the value of each of

a 49 ÷ 2.1 b 80.5 ÷ 3.9

.............................................................. ..............................................................

c 19.8 ÷ 3.2 d 617 ÷ 4.9

.............................................................. ..............................................................

4 Work out an estimate of the following and state whether your answer is an underestimate or overestimate.

a 499 × 68 b 7.1 × 20.68

.............................................................. ..............................................................

c 18.5 ÷ 4.1 d (21.8 ×11.06) ÷ 4.88

.............................................................. ..............................................................

Guided practice worksheet

Remember that 5.8 m is not 10 correct to 1 signi� cant � gure.

When you round up in the numerator and round down in the denominator, then you make the answer bigger.

D

Questions are targeted at the grades indicated

�2 3.5 Estimating calculations by rounding

83B

Guided practice worksheet

5 y = p(q + r) p = 17.8, q = 8.9, r = 12.75

Work out an estimate for the value of y.

......................................................................................................................

6 s v ua

=2 2

2− v = 4.8, u = 1.9, a = 21.1

Work out an estimate for the value of s.

......................................................................................................................

D

C

�2 3.6 Estimating calculations involving decimals

85A

1 Work out estimates for the values of the following.

a 6.8 × 0.48 ................................................................................... b 0.088 × 0.38 ................................................................................

........................................................................................................ ..........................................................................................................

c 0.75 × 0. 059 ............................................................................. d 0.0028 × 0.0788 .........................................................................

........................................................................................................ ..........................................................................................................

e 0.0682 ...........................................................................................

........................................................................................................

2 Work out estimates for the values of the following.

a 5.78 ÷ 0.601 .............................................................................. b 58. 99 ÷ 0.096 .............................................................................

........................................................................................................ ..........................................................................................................

c 199 ÷ 0.51 .................................................................................. d 0.333 ÷ 0. 641 .............................................................................

........................................................................................................ ..........................................................................................................

e 0.028 ÷ 0. 614 ..........................................................................

........................................................................................................

3 Work out estimates for the values of the following.

a 19 80 48

..

b 0 680 18..

.................................................................. ..................................................................

c 11 8 5 1

0 48. .

.××

d

0 81 4 890 102

. ..××

.................................................................. ..................................................................

e 0 791 789

0 203.

.×

..................................................................

Guided practice worksheet

When multiplying decimals count the total number of � gures after the decimal point.

When dividing by a decimal multiply both numbers to make the divisor a whole number.

D

C

Questions are targeted at the grades indicated

�2 3.6 Estimating calculations involving decimals

85B

Guided practice worksheet

4 Work out estimates for the values of the following. In each case state whether your answer is an overestimate or underestimate.

a 7.8 × 0.58 b 39 080 408

..

.................................................................. ..................................................................

c 19 120 208

2.. d

403 08 0 3060 398

. ..

×

.................................................................. ..................................................................

e 19 080 2082

..

..................................................................

5 A = πr 2 π = 3.142, r = 6.87

Work out an estimate for the value of A.

...........................................................................................................

6 v = ut + 0.5at2 u = 12.66, a = –0.57, t = 21.2

Work out an estimate for the value of v.

...........................................................................................................

7 y 2 = a + bx 2 a = 49.8, b = 0.48, x = 10.1

Work out an estimate for the value of y.

...........................................................................................................

8 h = 3 2Vrπ

π = 3.142, r = 0.891 , V = 9.09

Work out an estimate for the value of h.

...........................................................................................................

C

�2 3.7 Manipulating decimals

87A

1 Given that 5.6 × 23 = 128.8

work out

a 56 × 23 b 5.6 × 2.3 c 0.56 × 23 d 5.6 × 230

...................................

................................... ...................................

...................................

2 Given that 72 × 48 = 3456

work out

a 7.2 × 48 b 72 × 4800 c 0.72 × 48 d 72 × 4.8

...................................

................................... ...................................

...................................

3 Given that 15.9 × 7.6 = 120.84

work out

a 159 × 7.6 b 159 × 760 c 0.159 × 7.6 d 159 × 0.76

...................................

................................... ...................................

...................................

4 Given that 8.5 ÷ 6.8 = 1.25

work out

a 85 ÷ 6.8 b 0.85 ÷ 6.8 c 8.5 ÷ 68 d 8.5 ÷ 0.68

...................................

................................... ...................................

...................................

5 Given that 151.2 ÷ 6.3 = 24

work out

a 1512 ÷ 6.3 b 151.2 ÷ 63 c 151.2 ÷ 0.063 d 0.1512 ÷ 6.3

...................................

................................... ...................................

...................................

6 Given that 47.97 ÷ 7.8 = 6.15

work out

a 4797 ÷ 7.8 b 47.97 ÷ 780 c 4.797 ÷ 0.78 d 4797 ÷ 78

...................................

................................... ...................................

...................................

Guided practice worksheet

D

Questions are targeted at the grades indicated

�2 3.7 Manipulating decimals

87B

Guided practice worksheet

7 Given that 5 8 4 914

2 03. . .×× = = 2.03

work out

a 58 49

14××

b 5 8 4 9

1400. .××

c 0 58 490

14. ××

d

58 490140××

...................................

................................... ...................................

...................................

8 Given that 16 2 5 62 1

43 2. ..

.×× =

work out

a 162 56

2 1××

. b 16 2 5 6

210. .××

c

16 2 56210. ××

d

1 62 0 560 021

. ..××

...................................

................................... ...................................

...................................

C