AustraliaNSW
Stage 5.1-3

7.02 Accuracy and measurement

Worksheet
Units of measurement
1

State the most appropriate unit of measure for the following:

a

Height of a street pole.

b

Length of a highway.

c

Length of a phone strap.

d

Height of a cup.

e

Length of a horse.

f

Length of a country.

g

Height of a truck.

h

Length of a bus.

i

Length of the Amazon River.

j

Width of a USB.

k

Length of a fly.

l

Length of Australia's coastline.

m

n

Length of a train.

2

When measuring the length of a fingernail, what unit should we round to?

3

When measuring how far a person has jumped in the long jump, what unit should we round to?

Accuracy in measurement
4

Consider the image of a tape measure below:

a

What would you record for measurement P?

b

What is the absolute error of measurement P?

5

A measuring tape has markings every 20 \text{ cm}.

a

State the absolute error of the measuring tape.

b

The length of an object is measured as 120 \text{ cm} by the measuring tape. A second measurement is then taken, measuring its length to the nearest centimetre. What is the range we should expect this second measurement to lie within?

6

A scale has markings every 6 \text{ kg}.

a

State the absolute error of the scale.

b

The weight of an object is measured as 66 \text{ kg} by the scale. A second measurement is then taken, measuring its weight to the nearest kilogram. What is the range we should expect this second measurement to lie within?

7

A ruler has markings every 50 \text{ mm} along its length.

a

State the absolute error of the ruler's measurements.

b

An item is measured to be 350 \text{ mm} long with the ruler. What is the shortest length we should expect if its length is subsequently measured to the nearest millimetre?

8

A scale has markings every 0.5 \text{ g}.

a

State the absolute error of the scale's measurements.

b

An item is measured to weigh 4.5 \text{ g} with the scale. What is the largest weight we should expect if its weight is measured to the nearest hundredth of a gram?

9

The number of people at a concert is reported to be 52\,050. Can we determine the absolute error in the number of concert-goers? Explain your answer.

10

Consider the number 4464.

a

Round this number to:

i

One significant figure.

ii

Two significant figures.

b

Find the difference between these two rounded values.

11

The size of a concert crowd is measured to be 430\,000, to the nearest hundred. How many significant figures are there in the measured size of the concert crowd?

12

The length of a road is reported to be 100\,000 \text{ m} long. How many significant figures does this measurement contain if the length was measured to:

a

The nearest 1 kilometre?

b

The nearest 1 metre?

13

Pauline knows that her bedroom is roughly 3 \text{ m} long. To what precision must she measure if she wants to know the length to:

a

Two significant figures?

b

Four significant figures?

14

A rainfall gauge measures 261 \text{ mL} of rain, to the nearest millimetre. A nearby gauge has markings every 10 \text{ mL}. To how many significant figures would the rain be measured by this second gauge?

15

The volume of juice that can be squeezed from different bags of oranges is measured by four different tools, to get the following four different measurements:

• 1.163 \text{ L}
• 1074 \text{ mL}
• 934.3 \text{ mL}
• 927 \text{ mL}
16

Consider the following expression:

9.34 \text{ m} \times 8.160 \text{ m} \times 8.00 \text{ m}

a

How many significant figures does the least precise measurement have?

b

Calculate the result in cubic metres, rounding your answer to the least number of significant figures that you found in part (a).