Ordering (Copy)

Practice Questions – 1.5 Ordering

Question 1

Arrange the following numbers in ascending order:
7, −3, 12, 0, −8, 5

Question 2

Write using the correct symbol (>, <, =):
(a) 3/4 ___ 0.7
(b) √64 ___ 8
(c) −5 ___ −2

Question 3

Order the following fractions from smallest to largest:
2/3, 3/5, 5/8, 7/10

Question 4

Arrange in descending order:
0.25, 0.2, 0.202, 0.22, 0.222

Question 5

Insert the correct inequality symbol:
(a) 12 ÷ 4 ___ 5 − 2
(b) 3² ___ 2³
(c) 1/6 ___ 0.17

Question 6

Arrange the following in ascending order:
√2, √3, √5, 2.3

Question 7

Order the percentages:
48%, 4.8, 0.48, 480%

Question 8

A = 2/7, B = 3/10, C = 0.29
Order A, B, and C from smallest to largest.

Question 9

True or false?
(a) −7 < −9
(b) 0.333… = 1/3
(c) 2.5 > 5/2

Question 10

Arrange in descending order:
7/12, 5/8, 11/20, 9/15

Question 11

Insert the correct symbol (≥, ≤):
(a) n(A) ___ n(B) if A = {2, 4, 6} and B = {1, 2, 3, 4}
(b) −3 ___ −3
(c) 0.01 ___ 1/100

Question 12

Arrange these mixed forms in ascending order:
1/2, 0.55, 53%, 5/9

Question 13

Insert the correct symbol:
(a) |−12| ___ 10
(b) √50 ___ 7
(c) 3/8 ___ 0.4

Question 14

Arrange in order of size, smallest to largest:
3.01, 3.009, 3.099, 3.19, 3.9

Question 15

Compare and use = or ≠:
(a) 0.‾9 ___ 1
(b) 4/11 ___ 0.363636…
(c) 2/3 ___ 0.‾6

Answer key and explanations — 1.5 Ordering

1.

Ascending: −8, −3, 0, 5, 7, 12
Explanation: on the number line, more negative is smaller; then zero; then positives increasing.

2.

(a) 3/4 > 0.7
(b) √64 = 8
(c) −5 < −2
Explanation: 3/4 = 0.75; equal roots in (b); among negatives, the one closer to zero is greater.

3.

From smallest to largest: 3/5, 5/8, 2/3, 7/10
Explanation: as decimals: 0.6, 0.625, 0.666…, 0.7 respectively.

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4.

Descending: 0.25, 0.222, 0.22, 0.202, 0.2
Explanation: compare place values from left to right.

5.

(a) 12 ÷ 4 = 5 − 2
(b) 3² > 2³
(c) 1/6 < 0.17
Explanation: (a) both sides are 3; (b) 9 > 8; (c) 1/6 ≈ 0.166….

6.

Ascending: √2, √3, √5, 2.3
Explanation: √2 ≈ 1.414, √3 ≈ 1.732, √5 ≈ 2.236; all are less than 2.3 except 2.3 itself.

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course

7.

Order (by value) using percent-form for all: 0.48 = 48% < 4.8 = 480%
Explanation: 0.48 and 48% are equal (both 48 per hundred). Likewise, 4.8 equals 480%. So the complete ordering with ties is: 0.48 = 48% < 4.8 = 480%.

8.

Smallest to largest: A, C, B
Explanation: A = 2/7 ≈ 0.2857; C = 0.29; B = 3/10 = 0.3.

9.

(a) False (−7 is greater than −9)
(b) True (0.333… equals 1/3)
(c) False (2.5 = 5/2, so not greater)
Explanation: (c) convert 5/2 to 2.5 to compare.

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course

10.

Descending: 5/8, 9/15, 7/12, 11/20
Explanation: decimals: 5/8 = 0.625; 9/15 = 0.6; 7/12 ≈ 0.583; 11/20 = 0.55.

11.

(a) n(A) ≤ n(B)
(b) −3 ≥ −3
(c) 0.01 ≥ 1/100
Explanation: (a) sizes 3 and 4; (b) equality holds, so both ≥ and ≤ are true—either is acceptable; (c) 1/100 = 0.01, so equality again (≥ or ≤ both valid).

12.

Ascending: 1/2, 53%, 0.55, 5/9
Explanation: as decimals: 0.5, 0.53, 0.55, 0.555….

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course

13.

(a) |−12| > 10
(b) √50 > 7
(c) 3/8 < 0.4
Explanation: (a) absolute value gives 12; (b) √50 ≈ 7.071; (c) 3/8 = 0.375.

14.

Smallest to largest: 3.009, 3.01, 3.099, 3.19, 3.9
Explanation: align decimals to three places (3.009, 3.010, 3.099, 3.190, 3.900) and compare.

15.

(a) 0.‾9 = 1
(b) 4/11 = 0.363636…
(c) 2/3 = 0.‾6
Explanation: standard recurring decimal identities: 0.‾9 equals 1; 4/11 repeats 36; 2/3 repeats 6.