1.5.1 Try some yourself
Activity 9
Round 2098 765
(a) to 1 s.f.
(b) to 2 s.f.
(c) to 3 s.f.
(d) to 4 s.f.
Answer
(a) The first significant figure is 2. The next digit is 0, so round down. 2 098 765 = 2 000 000 (to 1 s.f.)
(b) The second significant figure is 0. The next digit is 9, so round up. 2 098 765 = 2 100 000 (to 2 s.f.)
(c) The third significant figure is 9. The next digit is 8, so round up. 2 098 765 = 2 100 000 (to 3 s.f.)
(d) The fourth significant figure is 8. The next digit is 7, so round up. 2 098 765 = 2 099 000 (to 4 s.f.)
Notice that in parts (b) and (c) the rounded numbers have the same value, but the precision is different. In part (b) there are two significant figures, namely 2 and 1, and in part (c) there are three, namely 2, 1 and 0. The zero is a significant figure here.
Activity 10
Has it ever occured to you how far planet Earth has travelled through the solar system during the last year, relative to the Sun, and how fast we earthlings are travelling?
In order to estimate this it is necessary to make some assumptions:
assume that the path of the Earth's orbit around the Sun is circular;
the distance between the Earth and the Sun is approximately 92 860 000 miles, which is the radius of the orbit;
distance travelled in one year is one orbit of the Sun;
the distance travelled along a circular path is determined by working out the circumference of a circle. The relationship between circumference and radius is: circumference = 2 ×
× radius.
So
distance travelled around Sun = 2 ×
× 92 860 000 miles.Using a calculator
button givesdistance = 583 456 587.6 miles.
(a) For convenience round this to two significant figures and write this in words.
(b) Given that the average speed is found by dividing the distance travelled by the time taken, estimate roughly how fast the Earth is travelling along its orbit around the Sun in miles per hour. (N.B. 1 year = 8760 hours.)
Answer
(a) 580 000 000 (to 2 s.f.), which is five hundred and eighty million miles.
(b) 580 000 000 miles in 8760 hours is 580 000 000 ÷ 8760 = 66 000 mph (to 2 s.f.)