What is N15: Rounding and error intervals?

Decimal places count digits after the decimal point; significant figures begin at the first non-zero digit. Identify the deciding digit immediately after the required place: 5 or more rounds up, while 4 or less leaves the retained digit unchanged.

How many marks are N15 questions worth?

In verified past-paper appearances, N15 questions on Edexcel GCSE Maths 1MA1 have been worth 1–5 marks.

Which past exam papers has N15 appeared in?

N15 has appeared in 36 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

N15

Round numbers and measures to an appropriate degree of accuracy (decimal places or significant figures); use inequality notation to specify simple error intervals due to truncation or rounding

Rounding and error intervals

Worked answers, methods and verified real exam appearances for N15 on Edexcel GCSE Maths 1MA1.

Explanation

Decimal places count digits after the decimal point; significant figures begin at the first non-zero digit. Identify the deciding digit immediately after the required place: $5$ or more rounds up, while $4$ or less leaves the retained digit unchanged.
Choose a degree of accuracy appropriate to the context, such as money to the nearest penny.
A rounded value also represents an error interval.
For rounding to a unit $u$ , subtract and add $\dfrac u2$ ; include the lower boundary but exclude the upper boundary because that endpoint rounds to the next value.
Truncation instead keeps values from the stated number up to the next truncation step.

The error interval for

12.6

correct to one decimal place.

Worked example

A positive number $y$ is truncated to $4.37$ at two decimal places. Write its error interval and find the greatest integer value of $100y$ .

1.Truncation gives $4.37\leq y<4.38$ .
2.Multiply the whole interval by $100$ : $437\leq100y<438$ .
3.The greatest integer in this interval is $437$ .

Answer: $4.37\leq y<4.38$ and the greatest integer value is $437$ .

Common mistakes

Don't count leading zeros as significant figures in $0.007846$ .
Don't include the upper boundary of a rounding interval.
Don't use half a rounding unit for a truncation interval.

Exam tip

State the rounding or truncation unit first; it determines both interval endpoints and which endpoint is excluded.

Worked practice

Tier 1 · Easy

Write

0.007846

correct to

2

significant figures.

(1)

(Total for Question 1 is 1 mark)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	$0.0078$	1	The first two significant digits are $7$ and $8$ . The next digit is $4$ , so the $8$ stays unchanged and the rounded value is $0.0078$ .

Tier 2 · Standard

A number

x

12.6

correct to

1

decimal place. Write the error interval for

x

(2)

(Total for Question 2 is 2 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	$12.55\leq x<12.65$	2	The rounding unit is $0.1$ , so half a unit is $0.05$ . Subtract and add $0.05$ to get the boundaries $12.55$ and $12.65$ ; include the lower boundary only.

Tier 3 · Hard

A positive number

y

is truncated to

4.37

2

decimal places. Write its error interval and find the greatest possible integer value of

100y

(3)

(Total for Question 3 is 3 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	$4.37\leq y<4.38$ Greatest possible integer value of $100y$ is $437$ .	3	Truncation to $2$ decimal places keeps every value from $4.37$ up to but not including $4.38$ , so $4.37\leq y<4.38$ . Multiplying by $100$ gives $437\leq100y<438$ , whose greatest possible integer value is $437$ .

Tier 1 · Easy

Write

53\,749

correct to

2

significant figures.

(1)

(Total for Question 4 is 1 mark)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$54\,000$	1	The first two significant digits are $5$ and $3$ . The next digit is $7$ , so round the $3$ up to $4$ to get $54\,000$ .

Tier 2 · Standard

A number

n

730

correct to the nearest

10

. Write the error interval for

n

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$725\leq n<735$	2	Half of the rounding unit $10$ is $5$ . The lower boundary is $730-5=725$ and is included; the upper boundary is $730+5=735$ and is excluded.

Tier 3 · Hard

A length is

155

mm correct to the nearest

5

mm. Salma writes

152.5<x\leq157.5

. Write the correct error interval and explain both changes to Salma's inequality signs.

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	$152.5\leq x<157.5$ ; $152.5$ is included because it rounds to $155$ mm, but $157.5$ is excluded because it rounds to $160$ mm.	3	Half of the rounding unit $5$ mm is $2.5$ mm. The lower bound $152.5$ mm rounds to $155$ mm, so it is included. The upper bound $157.5$ mm rounds to $160$ mm, so it is excluded. Hence $152.5\leq x<157.5$ .

Tier 2 · Standard

Write

12.4867

correct to

3

significant figures and correct to

2

decimal places.

(2)

(Total for Question 7 is 2 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	$12.5$ to $3$ significant figures and $12.49$ to $2$ decimal places	2	For $3$ significant figures, keep $1,2,4$ and use the next digit $8$ , giving $12.5$ . For $2$ decimal places, keep $12.48$ and use the next digit $6$ , giving $12.49$ .

Tier 3 · Hard

A positive number

x

2.4

correct to

1

decimal place. Work out all the possible integer values of

20x

(3)

(Total for Question 8 is 3 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	$47$ and $48$	3	$2.35\leq x<2.45$ . Multiplying the interval by $20$ gives $47\leq20x<49$ . The integer values in this interval are $47$ and $48$ .

Tier 3 · Hard

A positive number

x

0.008

correct to

1

significant figure and

0.0076

correct to

2

significant figures. Write the error interval for

x

that satisfies both statements.

(4)

(Total for Question 9 is 4 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	$0.00755\leq x<0.00765$	4	The first statement gives $0.0075\leq x<0.0085$ . The second gives the narrower interval $0.00755\leq x<0.00765$ , which lies wholly inside the first interval. Their intersection is therefore $0.00755\leq x<0.00765$ .

Q10

Tier 3 · Hard

A positive integer is

68\,000

correct to

2

significant figures. The integer is a multiple of

400

. Work out the least and the greatest possible values of the integer.

(4)

(Total for Question 10 is 4 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	Least $=67\,600$ ; greatest $=68\,400$ .	4	The rounding interval is $67\,500\leq n<68\,500$ . The first multiple of $400$ in this interval is $67\,600$ . The last is $68\,400$ , because the next multiple, $68\,800$ , is outside the interval.

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2019-06	3H	Q7	2	Allowed	Higher	QP MS
2019-06	3F	Q1	1	Allowed	Foundation	QP MS
2022-06	2F	Q1	1	Allowed	Foundation	QP MS
2023-11	3F	Q2	1	Allowed	Foundation	QP MS
2022-06	2H	Q8	2	Allowed	Higher	QP MS
2019-06	2H	Q6	2	Allowed	Higher	QP MS
2022-06	2F	Q23	2	Allowed	Foundation	QP MS
2023-06	2F	Q1	1	Allowed	Foundation	QP MS
2021-11	1H	Q10	4	Non-calculator	Higher	QP MS
2019-11	1F	Q2	1	Non-calculator	Foundation	QP MS
2022-06	3H	Q16	3	Allowed	Higher	QP MS
2019-11	2F	Q2	1	Allowed	Foundation	QP MS
2021-11	3H	Q11	2	Allowed	Higher	QP MS
2019-11	2H	Q2	2	Allowed	Higher	QP MS
2024-06	1F	Q1	1	Non-calculator	Foundation	QP MS
2024-11	3H	Q7	2	Allowed	Higher	QP MS
2022-11	3H	Q12	2	Allowed	Higher	QP MS
2019-06	2F	Q25	2	Allowed	Foundation	QP MS
2021-11	1F	Q27	2	Non-calculator	Foundation	QP MS
2019-11	3H	Q2	3	Allowed	Higher	QP MS
2023-11	2F	Q18	3	Allowed	Foundation	QP MS
2019-11	3F	Q23	3	Allowed	Foundation	QP MS
2021-11	2F	Q12	3	Allowed	Foundation	QP MS
2022-11	2F	Q25	3	Allowed	Foundation	QP MS
2022-11	3F	Q4	1	Allowed	Foundation	QP MS
2022-06	2H	Q3	2	Allowed	Higher	QP MS
2019-06	3H	Q19	5	Allowed	Higher	QP MS
2022-11	3F	Q17	3	Allowed	Foundation	QP MS
2024-06	2H	Q9	2	Allowed	Higher	QP MS
2023-06	2H	Q7	2	Allowed	Higher	QP MS
2023-06	2F	Q26	2	Allowed	Foundation	QP MS
2023-11	2H	Q8	2	Allowed	Higher	QP MS
2022-06	3F	Q18	2	Allowed	Foundation	QP MS
2019-11	2F	Q22	2	Allowed	Foundation	QP MS
2024-06	2F	Q19	3	Allowed	Foundation	QP MS
2021-11	1F	Q4	1	Non-calculator	Foundation	QP MS

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