AustraliaNSW
Stage 5.1-3

# 7.01 Significant figures

Worksheet
Count significant figures
1

State the number of significant figures in the following numbers:

a
108\,486
b
5105
c
0.20
d
10.20
e
84.00
f
0.007\,1930
g
0.004\,58
h
2.0058
i

2.84

j

0.063

k

0.087\,700

l

54\,100

m

157\,422.856\,760

2

State the smallest possible number of significant figures in the following numbers:

a
1\,500\,000
b
26\,500
c
1\,060\,000
d
82\,420\,000
3

A rainfall gauge has markings every 10\text{ mL}. If 369\text{ mL} of rain fell in this gauge, to how many significant figures would the rain be recorded?

4

Beth just bought a house for \$858\,400. When asked for the price by her friend, she said she paid around \$860\,000. To how many significant figures did Beth round the price in her answer?

Round to significant figures
5

Consider the number 1083.

a

Round 1083 to:

i

One significant figure

ii

Two significant figures

b

Find the difference between these two rounded values.

6

Round the following numbers to two significant figures:

a
2584
b
10\,694
c
9249
d
215.99
e
0.7218
f
0.0297
g
4.95
h
0.006\,037\,736
7

Round the following numbers to three significant figures:

a
1771
b
461\,585
c
6484
d
20\,994
e
9248
f
539.99
g
0.5628
h
0.073\,582
i
323\,385.794\,850
8

Round the following numbers to four significant figures:

a
801\,600\,713
b
0.060\,070\,047
9

Round the following numbers to five significant figures:

a
645\,129
b
7231.0108
10

Express the fraction \dfrac{13}{7} as a decimal to five significant figures.

11

Express the fraction \dfrac{2}{35} as a decimal to four significant figures.

12

Calculate the following and give your answers to an appropriate number of significant figures:

a

1.4 \times 1.41

b

3.9488 \times 1.21

c

\dfrac{7.8}{2.65}

d

\dfrac{6.1236}{1.93}

13

Use your calculator to round the following to three significant figures:\dfrac{\left(9.45\right)^{9} + 8 \pi}{\sqrt{\left(\dfrac{3}{2} + 5^{2}\right)}}

14

A number has been rounded to two significant figures. If the rounded number is 4500, find the largest possible integer value of the original number.

15

A number has been rounded to two significant figures. If the rounded number is 8700, find the largest possible integer value of the original number.

16

The population of a small town has been reported as 5000 people.

a

Could the population of the town have been rounded to two significant figure? Explain your answer.

b

If the population number has been rounded to two significant figures, state the largest and smallest populations.

c

If the population number has been rounded to one significant figure, state the largest and smallest populations.