1.4.1 Try some yourself
Activity 8
If a litre is one cubic decimetre, how many litres are there in a cubic metre?
Answer
Since a litre is one cubic decimeter, the question is asking how may cubic decimetres are in a cubic metre.
1 metre = 10 decimetres
so 1 m3 = 103 cubic decimetres.
Hence there are 1000 litres in a cubic metre.
Activity 9
Find the following without using your calculator, as an estimate for the calculator work in the next question.
(a) (−1)3
(b) 33
(c) 1003
(d) 0.13
Answer
(a) (−1)3 = −1 × −1 × −1 = 1 × −1 = −1
(b) 33 = 3 × 3 × 3 = 9 × 3 = 27
(c) 1003 = 100 × 100 × 100 = 10 000 × 100 = 1000 000 (a million)
(d)
Activity 10
Use your calculator to find the following.
(a) (−1.2)3
(b) 3.33
(c) 1013
(d) 0.1213
Answer
(a) Estimate: (−1)3 = −1.
Calculate: (−1.2)3 = −1.728.
(b) Estimate: 33 = 27.
Calculate: 3.33 = 35.937.
(c) Estimate: 1003 = 1000 000.
Calculate: 1013 = 1030 301.
(d) Estimate: .13 = .001.
Calculate: 0.1213 = 0.00177 (3 s.f.)
Activity 11
What are the following?
(a)
(b)
Answer
(a)
= 1 since 13 = 1.(b)
= 10 since 103 = 1000.
Activity 12
Find the volume of a one-foot cube in cubic metres (1 foot = 30.48 cm). Estimate your answer first. Round your answer to three decimal places.
Answer
To estimate an answer, choose a simple approximation, say
1 foot 
30 cm = 0.3 m.
Then 1 foot cubed (0.3)3 = 0.027 m3.
More accurately, 1 foot = 30.48 cm = 0.3048 m.
So 1 foot cubed = (0.3048)3 = 0.028 m3 to three d.p.
Activity 13
Without using your calculator, find the following, as estimates for the calculator work in Question 7.
(a) 92
(b) 43
(c)
(d)
(e) (−3)2
Answer
(a) 92 = 9 × 9 = 81
(b) 43 = 4 × 4 × 4 = 16 × 4 = 64
(c)
= 8 (since 82 = 64)(d)
(e) (−3)2 = −3 × −3 = 9
Activity 14
Use your calculator to find:
(a) 9.422
(b) 3.653
(c)
(d) 0.333
(e) (−2.713)2
Use your answers to the previous question as rough checks. Round your answers to four decimal places.
Answer
(a) 9.422 = 88.7364
(b) 3.653
48.6271(c)
8.3666(d) 0.333
0.0359 (check this by calculating 
, the estimate from 3(d) above, as a decimal.(e) (−2.713)2
7.3604 (N.B. To get this answer on a calculator, remember the brackets.)