KS3 Maths · Year 7 · Chapter 8: Number · Lesson 2

Significant figures

Year 7About 60 minutesCalculator allowed48 marks

Hints online, answers free with an account:
mathswariz.uk/worksheets/ks3-year-7-significant-figures/

Date

Do Now

Quick questions to start.

A1
Needed today
Round $4728$ to the nearest hundred.
[1 mark]
Answer
A2
Needed today
Round $6.374$ to $1$ decimal place.
[1 mark]
Answer
A3
Last lesson
Work out $4.7 \times 1 0^{- 2}$ .
[1 mark]
Answer
A4
From chapter 4
Increase £80 by $5%$ .
[1 mark]
Answer

Example, then your turn

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

Round each number.

(a) $8627$ to $1$ significant figure (1 sf)

(b) $46381$ to $2$ significant figures (2 sf).

Hint Find the first non-zero digit. Look at the digit after the last one you keep:

5

or more rounds up. Fill the rest of the places with zeros.

B1
Round each number.
(a) $3482$ to $1$ sf (b) $72950$ to $2$ sf
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 2

Round each number.

(a) $0.047 18$ to $2$ sf (b) $0.6352$ to $1$ sf

Hint In a number less than

1

, the zeros at the front are not significant. Start counting at the first digit that is not zero.

B2
Round each number.
(a) $0.003 851$ to $2$ sf (b) $0.0726$ to $1$ sf
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 3

Round each number.

(a) $7.396$ to $3$ sf (b) $0.049 96$ to $2$ sf

Hint When

39

rounds up it becomes

40

. Keep the zero at the end: it is one of the significant figures asked for.

B3
Round each number.
(a) $2.4983$ to $3$ sf (b) $30.97$ to $3$ sf
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

Example 4

A machine fills $13$ bottles in $50$ seconds. Work out the time it takes to fill one bottle. Give your answer to $2$ sf

Hint Use a calculator. The full answer has far too many figures for a time, so round it.

B4
A $2$ kg bag of rice is shared equally between $7$ pots. Work out the mass of rice in each pot, in grams. Give your answer to $3$ sf
[2 marks]
Answer

Example 5

The crowd at a football match is $28000$ , correct to $2$ significant figures. Write down the smallest and the largest number of people there could have been.

Hint To

2

significant figures means to the nearest thousand here. Half a thousand either way.

B5
The number of people at a concert is $6000$ , correct to $1$ significant figure. Write down the least and the greatest number of people there could have been.
[2 marks]
Answerleast $\dots\dots$ greatest $\dots\dots$

Practice

Year 7

C1
How many significant figures does each number have?
(a) $4.07$ (b) $0.0062$ (c) $3.40$
[3 marks]
Answer(a) $\dots$ (b) $\dots$ (c) $\dots$
C2
Round each number.
(a) $99.62$ to $2$ sf (b) $0.9973$ to $2$ sf
[2 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$

C3
Round each number to $1$ significant figure to estimate the value of $\frac{61.8 \times 3.94}{0.213}$
[2 marks]
Answer
C4
The table shows the visitors to three places in one year. Round the visitors to
(a) River Gallery to $2$ sf (b) Castle to $1$ sf (c) Hill Museum to $3$ sf
[3 marks]
Answer(a) $\dots\dots$ (b) $\dots\dots$ (c) $\dots\dots$
C5
Use a calculator to work out $57.3$ . Give your answer to $3$ sf
[1 mark]
Answer

Exam-style questions

GCSE Foundation

D1
Answer each part.
(a)
Round $0.073 49$ to $2$ sf
[1 mark]
Answer
(b)
Round $52718$ to $3$ sf
[1 mark]
Answer
Total for D1: 2 marks

D2
Ella rounds $0.0307$ to $2$ significant figures. She writes $0.03$ .
Explain why Ella is wrong. Write down the correct answer.
[2 marks]
Answer
D3
A factory makes $2385$ boxes of pens each day. Each box holds $48$ pens.
(a)
By rounding each number to $1$ significant figure, estimate the number of pens the factory makes in one day.
[2 marks]
Answer
(b)
Work out the exact number of pens the factory makes in $5$ days.
[2 marks]
Answer
(c)
Write your answer to part (b) correct to $2$ sf
[1 mark]
Answer
Total for D3: 5 marks
D4
A festival lasts two days. The number of people on Saturday is $14000$ , correct to $2$ significant figures. The number of people on Sunday is $9000$ , correct to $1$ sf
(a)
Work out the least possible total number of people over the two days.
[2 marks]
Answer
(b)
Work out the greatest possible total number of people over the two days.
[2 marks]
Answer
Total for D4: 4 marks
D5
Use your calculator to work out $\frac{18. 7 ^{2} - 4.36}{29.2}$
(a)
Write down all the figures on your calculator display.
[2 marks]
Answer
(b)
Write your answer to part (a) correct to $3$ sf
[1 mark]
Answer
Total for D5: 3 marks
D6
Tickets for a show cost £19.75 each. A school buys $31$ tickets.
(a)
Estimate the total cost by rounding each number to $1$ sf
[1 mark]
Answer
(b)
Is your estimate too big or too small? Work out the exact cost to check. Give a reason for your answer.
[2 marks]
Answer
Total for D6: 3 marks

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
A whole number rounds to $4000$ when it is rounded to $1$ significant figure. The same number rounds to $3500$ when it is rounded to $2$ significant figures. Work out the smallest and the largest number it could be.
[4 marks]
Hint 1 · What to try
Write down all the whole numbers that round to $4000$ to $1$ significant figure. Then do the same for $3500$ to $2$ sf
Hint 2 · The first line
To $1$ significant figure: from $3500$ up to $4499$ . To $2$ significant figures: from $3450$ up to $3549$ .
Hint 3 · The full method
The number is in both lists, so it is from $3500$ up to $3549$ . Smallest $3500$ , largest $3549$ .
Answersmallest $\dots\dots$ largest $\dots\dots$

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can count the significant figures in a number.
I can round a number to $1$ , $2$ or $3$ sf
I can choose a sensible accuracy and estimate a calculation.
I can find the smallest and largest value of a rounded number.

Answers and mark scheme

The worked answers and the full mark scheme are free with a Mathswariz account. Teachers and students can both sign up.

Get the answers