Q2. Write each of the following number correct to 3 significant figures:
(a) 0.0025713 (b) 18.3071 (c) 4.0071 (d) 0.3684
Answers
Step-by-step explanation:
Note that a measured length such as '12 cm to the nearest cm' means that the actual length lies between 11.5 cm and 12.5 cm.
By convention, we normally round 0.5 up to the next whole number, so in fact,
11.5 cm ≤ actual length < 12.5 cm
We call 11.5 the lower bound and 12.5 the upper bound. We can also write the upper bound as
12.4999 . . . . or 12.49
where the dot above the 9 means that it is repeated indefinitely, or recurs.
It is important to see that 12.49 is not the upper bound, as, for example, the length could have been 12.498.
Example 1
A football match is watched by 56 742 people. Write this number correct to the nearest,
(a) 10 000,
(b) 1000,
(c) 10.
Example 2
Write each of the following numbers correct to 3 significant figures:
(a) 47 316
(b) 303 971
(c) 20.453
(d) 0.004368
Example 3
Write each of the following numbers correct to the number of decimal places stated:
(a) 0.3741 to 2 d.p.
(b) 3.8451 to 2 d.p.
(c) 142.8315 to 1 d.p.
(d) 0.000851 to 4 d.p.
Example 4
State the upper and lower bounds for each of the following quantities and write an inequality for the actual value in each case.