What is N1: Order numbers?

Integers, decimals and fractions can be ordered once they are written in a comparable form.

How many marks are N1 questions worth?

In verified past-paper appearances, N1 questions on Edexcel GCSE Maths 1MA1 have been worth 1–5 marks.

Which past exam papers has N1 appeared in?

N1 has appeared in 28 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

Order positive and negative integers, decimals and fractions; use the symbols =, ≠, <, >, ≤, ≥

Order numbers

Worked answers, methods and verified real exam appearances for N1 on Edexcel GCSE Maths 1MA1.

Explanation

Integers, decimals and fractions can be ordered once they are written in a comparable form.
Convert fractions to decimals, or use a common denominator, then place the values on a number line: values increase from left to right.
This is especially important for negatives, because the number with the greater distance below zero is smaller; for example, $-1.7<-\dfrac{3}{2}$ since $-1.7<-1.5$ .
Use $=$ for equal values, $\neq$ for unequal values, and read $\leq$ or $\geq$ as allowing equality.
In an exam, show the conversion that justifies each comparison.

A number line showing that

-1.85

lies to the left of

-1.75

Worked example

Write $-\dfrac{7}{4}$ , $-1.68$ , $\dfrac{5}{3}$ and $1.7$ in ascending order.

1.Convert the fractions: $-\dfrac{7}{4}=-1.75$ and $\dfrac{5}{3}=1.666\ldots$ .
2.Compare the negative values first: $-1.75<-1.68$ .
3.Compare the positive values: $1.666\ldots<1.7$ , then write the complete ordered list.

Answer: $-\dfrac{7}{4},\ -1.68,\ \dfrac{5}{3},\ 1.7$ .

Common mistakes

Don't write $-8>-3$ because $8>3$ , ignoring that $-8$ lies farther left.
Don't treat $\leq$ as meaning strictly less than and reject the equal endpoint.
Don't round a recurring decimal too early and change the intended order.

Exam tip

For a 2-mark ordering question, show decimal or common-denominator conversions before the final list.

Worked practice

Tier 1 · Easy

Insert either

<

>

=

between

-0.62

and

-\dfrac{3}{5}

(1)

(Total for Question 1 is 1 mark)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	$-0.62<-\dfrac{3}{5}$	1	Convert $-\dfrac{3}{5}$ to $-0.6$ . Since $-0.62$ is farther left on the number line than $-0.6$ , $-0.62<-\dfrac{3}{5}$ .

Tier 2 · Standard

Mia says that

-6>-2

because

6>2

. Explain why Mia is wrong.

(2)

(Total for Question 2 is 2 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	$-6<-2$ because $-6$ lies farther to the left on a number line.	2	For negative numbers, the number with the greater distance below zero is smaller. Since $-6$ is farther left than $-2$ , the correct comparison is $-6<-2$ .

Tier 3 · Hard

An integer

k

satisfies

-2.4<\dfrac{k}{3}\leq1.7

. Write down every possible value of

k

(3)

(Total for Question 3 is 3 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	$k=-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5$	3	Multiply every part by positive $3$ , so the inequality signs stay unchanged: $-7.2<k\leq5.1$ . The integers in this interval are $-7$ through $5$ inclusive.

Tier 1 · Easy

Write

-0.47

-\dfrac{9}{20}

-0.52

and

-\dfrac{1}{2}

in ascending order.

(2)

(Total for Question 4 is 2 marks)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$-0.52,\ -\dfrac{1}{2},\ -0.47,\ -\dfrac{9}{20}$	2	$-\dfrac{9}{20}=-0.45$ and $-\dfrac{1}{2}=-0.5$ . From smallest to greatest, the values are $-0.52,-0.5,-0.47,-0.45$ .

Tier 2 · Standard

Write

-1.2

-\dfrac{7}{6}

and

-1.15

in descending order.

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$-1.15,\ -\dfrac{7}{6},\ -1.2$	2	$-\dfrac{7}{6}=-1.1666\ldots$ . For negative numbers, the value closest to zero is greatest, so the descending order is $-1.15,-1.1666\ldots,-1.2$ .

Tier 3 · Hard

Sam writes

-\dfrac{13}{20}<-0.66<-\dfrac{2}{3}

. Is Sam correct? Give a reason.

(2)

(Total for Question 6 is 2 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	No; the correct order is $-\dfrac{2}{3}<-0.66<-\dfrac{13}{20}$ .	2	Use denominator $300$ : $-\dfrac{2}{3}=-\dfrac{200}{300}$ , $-0.66=-\dfrac{198}{300}$ and $-\dfrac{13}{20}=-\dfrac{195}{300}$ . Therefore $-\dfrac{2}{3}<-0.66<-\dfrac{13}{20}$ , so Sam is not correct.

Tier 2 · Standard

The box in

-0.6\square

is filled with one digit. The completed decimal is greater than

-0.64

and less than

-0.58

. Work out all the possible digits.

(3)

(Total for Question 7 is 3 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	$0,1,2,3$	3	The completed decimal must lie between $-0.64$ and $-0.58$ . The values $-0.60$ , $-0.61$ , $-0.62$ and $-0.63$ all do this, whereas $-0.64$ is not greater than the lower endpoint. The possible digits are $0,1,2,3$ .

Tier 3 · Hard

Four cards show

-\dfrac{11}{18}

-0.605

-61\%

and

-0.59

. Work out the difference between the greatest value and the smallest value. Give your answer as a fraction.

(4)

(Total for Question 8 is 4 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	$\dfrac{19}{900}$	4	$-\dfrac{11}{18}=-0.6111\ldots$ and $-61\%=-0.61$ . The greatest value is $-0.59$ and the smallest is $-\dfrac{11}{18}$ . Their difference is $-\dfrac{59}{100}+\dfrac{11}{18}=\dfrac{38}{1800}=\dfrac{19}{900}$ .

Tier 3 · Hard

Points

P

Q

R

and

S

have coordinates

-\dfrac{3}{4}

-0.72

-73\%

and

-\dfrac{7}{10}

respectively. Which points lie in the interval

-0.74<x\leq-0.71

? Write their coordinates in descending order.

(3)

(Total for Question 9 is 3 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	$Q$ and $R$ ; $-0.72,\ -73\%$ (or $-0.72,\ -0.73$ )	3	$P=-0.75$ , $R=-0.73$ and $S=-0.70$ . Only $Q=-0.72$ and $R=-0.73$ lie in the stated interval. Since $-0.72>-0.73$ , their coordinates in descending order are $-0.72,-0.73$ .

Q10

Tier 3 · Hard

The integer

k

satisfies

-0.56<-\dfrac{k}{40}<-0.54

. Work out

k

. You must show all your working.

(3)

(Total for Question 10 is 3 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	$k=22$	3	Multiplying by $40$ gives $-22.4<-k<-21.6$ . Multiplying by $-1$ reverses both inequality signs, so $21.6<k<22.4$ . The only integer in this interval is $22$ .

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2022-11	2F	Q1	1	Allowed	Foundation	QP MS
2023-06	3F	Q5	1	Allowed	Foundation	QP MS
2022-06	1F	Q5	1	Non-calculator	Foundation	QP MS
2019-06	2F	Q16	5	Allowed	Foundation	QP MS
2021-11	2F	Q3	1	Allowed	Foundation	QP MS
2022-11	3H	Q11	2	Allowed	Higher	QP MS
2024-06	2F	Q1	1	Allowed	Foundation	QP MS
2022-11	2F	Q12	4	Allowed	Foundation	QP MS
2021-11	1F	Q2	1	Non-calculator	Foundation	QP MS
2019-06	2F	Q10	2	Allowed	Foundation	QP MS
2021-11	2H	Q1	3	Allowed	Higher	QP MS
2023-11	3F	Q3	1	Allowed	Foundation	QP MS
2024-11	2F	Q3	1	Allowed	Foundation	QP MS
2022-11	3F	Q1	1	Allowed	Foundation	QP MS
2019-06	2F	Q5	1	Allowed	Foundation	QP MS
2019-06	1F	Q8	2	Non-calculator	Foundation	QP MS
2021-11	2F	Q15	2	Allowed	Foundation	QP MS
2024-06	3F	Q5	1	Allowed	Foundation	QP MS
2024-06	1F	Q4	1	Non-calculator	Foundation	QP MS
2023-06	1F	Q3	1	Non-calculator	Foundation	QP MS
2022-11	3F	Q2	1	Allowed	Foundation	QP MS
2022-06	1F	Q4	1	Non-calculator	Foundation	QP MS
2022-06	2F	Q14	2	Allowed	Foundation	QP MS
2022-06	2F	Q6	1	Allowed	Foundation	QP MS
2019-06	2F	Q2	1	Allowed	Foundation	QP MS
2024-11	3F	Q4	1	Allowed	Foundation	QP MS
2023-11	3F	Q14	2	Allowed	Foundation	QP MS
2019-11	2F	Q1	1	Allowed	Foundation	QP MS

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