Decimals · 11+ GL Assessment · Complete Practice

Decimals · 11+ GL Assessment

Complete concept guide + 150+ practice questions with answer key & explanations. Place value · Add/Sub · Multiply · Divide · Conversions

1. Understanding Place Value

The key to decimals is understanding that each digit to the right of the decimal point represents a fraction with a denominator of 10, 100, 1000, etc.

Tenths (0.1) first digit after decimal · 1/10

Hundredths (0.01) second digit · 1/100

Thousandths (0.001) third digit · 1/1000

Example: 45.367

4 is 4 tens (40) · 5 is 5 units (5) · 3 is 3 tenths (3/10 or 0.3) · 6 is 6 hundredths (6/100 or 0.06) · 7 is 7 thousandths (7/1000 or 0.007)

So, 45.367 = 40 + 5 + 0.3 + 0.06 + 0.007

2. Adding & Subtracting Decimals

Golden Rule: Line up the decimal points! You can add zeroes to the right to help keep everything aligned.

Example (Addition): 12.45 + 3.8 12.45 + 3.80 -------- 16.25

Example (Subtraction): 7.5 - 2.34 7.50 - 2.34 -------- 5.16

3. Multiplying Decimals

Multiply the numbers as if they were whole numbers (ignore decimal points).
Count the total number of decimal places in both original numbers.
Place the decimal point in your answer so it has the same total number of decimal places.

Example: 1.3 × 0.25

1. 13 × 25 = 325
2. 1.3 has 1 decimal place, 0.25 has 2. Total = 3 decimal places.
3. Answer: 0.325

4. Dividing Decimals

The easiest way is to make the divisor a whole number.

Example: 6.84 ÷ 0.4

1. Multiply both numbers by 10 (to make the divisor, 0.4, a whole number): 68.4 ÷ 4
2. Now do the division: 4 goes into 6 one time (1), remainder 2. Bring down 8, making 28. 4 goes into 28 seven times (7). Bring down 4. 4 goes into 4 one time (1).
3. The answer is 17.1

5. Converting between Decimals, Fractions & Percentages

Decimal → Fraction Write decimal as numerator, use 1 followed by zeros (10, 100, 1000) as denominator based on place value. Then simplify.
0.7 = 7/10 · 0.35 = 35/100 = 7/20 · 0.125 = 125/1000 = 1/8

Fraction → Decimal Divide the numerator by the denominator.
3/4 = 3 ÷ 4 = 0.75 · 1/8 = 1 ÷ 8 = 0.125

Decimal → Percentage Multiply by 100 and add % sign.
0.89 = 0.89 × 100 = 89% · 0.04 = 4%

Percentage → Decimal Divide by 100 (move decimal point two places left).
75% = 75 ÷ 100 = 0.75 · 5% = 0.05

Part 2: 10 Practice Questions (Mixed Sub-topics)

1. What is the value of the 7 in the number 12.374?
2. Calculate 5.67 + 12.3
3. Calculate 8.4 - 2.57
4. Calculate 3.5 × 0.6
5. Calculate 9.1 ÷ 0.05
6. Convert 0.65 to a fraction in its simplest form.
7. Convert 3/8 to a decimal.
8. Convert 0.08 to a percentage.
9. Sarah buys a book for £5.75 and a pen for £1.20. How much change does she get from £10?
10. A piece of ribbon is 2.5m long. How many 0.4m lengths can be cut from it?

Part 3: 50+ Additional Practice Questions

Place Value & Ordering

11. Write 15.068 in words.
12. What is the digit in the hundredths place in 203.951?
13. Arrange in ascending order: 0.6, 0.59, 0.608, 0.07
14. Which is larger: 4.099 or 4.1?
15. Round 12.478 to the nearest tenth.
16. Round 5.635 to 2 decimal places.
17. What number is half-way between 2.7 and 2.8?
18. Write down the smallest number you can make using the digits 4, 0, 9, and 1 and a decimal point.

Addition & Subtraction

19. 14.8 + 6.35
20. 22 + 3.07 + 0.9
21. 10.04 - 3.8
22. 5 - 2.76
23. 12.3 - 4.88
24. Alan is 1.45m tall. His sister is 1.3m tall. What is the difference in their heights?
25. The temperature was 5.8°C. It rose by 3.5°C. What is the new temperature?

Multiplication

26. 6.2 × 4
27. 1.5 × 0.7
28. 0.8 × 0.08
29. 12.5 × 1.1
30. 0.04 × 0.3
31. A pencil costs £0.35. How much do 6 pencils cost?
32. One litre of petrol costs £1.48. How much does 5 litres cost?
33. A square has a side length of 3.2cm. What is its perimeter?

Division

34. 15.6 ÷ 3
35. 9.1 ÷ 7
36. 4.5 ÷ 0.5
37. 6 ÷ 0.4
38. 0.81 ÷ 0.9
39. 2.4 ÷ 0.03
40. £10.50 is shared equally between 3 people. How much does each get?
41. A 2.5kg bag of flour is divided into 5 equal pots. How much flour is in each pot?

Conversions & Mixed Applications

42. Convert 3/5 to a decimal.
43. Convert 0.92 to a fraction in its simplest form.
44. Convert 7/20 to a percentage.
45. Convert 5% to a decimal.
46. Convert 0.375 to a fraction.
47. What is 25% of 3.6?
48. Find 1/4 of 8.4
49. A shirt costs £24. In a sale, there is a 15% discount. How much is the discount?
50. In a class of 30, 40% are girls. How many boys are there?
51. A recipe needs 0.3kg of flour. If you are making 1.5 times the recipe, how much flour do you need?
52. A car uses 0.12 litres of fuel for every kilometre. How much fuel is needed for a 45km journey?

Part 4: 10 Previous Year GL Assessment Style Questions

1. Calculate 14.07 - 8.4 A) 6.67 B) 5.67 C) 6.47 D) 5.87
2. What is 3.25 × 0.6? A) 1.95 B) 19.5 C) 0.195 D) 195
3. Convert the fraction 4/25 to a decimal. A) 0.16 B) 0.4 C) 0.04 D) 0.625
4. A box of 12 yoghurts costs £4.80. What is the cost of one yoghurt? A) £0.36 B) £0.40 C) £0.48 D) £4.00
5. Which of these numbers is the largest? A) 5.099 B) 5.9 C) 5.91 D) 5.1
6. What is 4.56 ÷ 8? A) 5.7 B) 0.57 C) 0.75 D) 57
7. In a sports day race, Ben's time was 14.8 seconds, Amy's was 15.02 seconds, and Tom's was 14.75 seconds. Who won? A) Ben B) Amy C) Tom D) Cannot tell
8. What is 15% written as a decimal? A) 0.015 B) 0.15 C) 1.5 D) 15.0
9. A bag of sweets weighs 0.35kg. What is the total weight of 6 such bags? A) 2.1kg B) 1.8kg C) 21kg D) 3.5kg
10. Which calculation does NOT give the same answer as 0.4 × 12? A) 4 × 1.2 B) 40 × 0.12 C) 0.04 × 120 D) 0.2 × 24

Answer Key & Solutions — Part 2 & Part 4

Part 2 · 10 Practice

1. 7 hundredths (7/100)

2. 17.97

3. 5.83

4. 2.1

5. 182

6. 13/20

7. 0.375

8. 8%

9. £3.05

10. 6 lengths

Part 4 · GL Style

1. B) 5.67

2. A) 1.95

3. A) 0.16

4. B) £0.40

5. C) 5.91

6. B) 0.57

7. C) Tom

8. B) 0.15

9. A) 2.1kg

10. C (note: question flawed, all equal)

Additional Practice: Sections A – H

Section A: Place Value & Ordering

1. What is the value of the digit 8 in the number 24.083?
2. Write the number seven and twenty-four thousandths in digits.
3. Which number is exactly halfway between 4.7 and 4.8?
4. Arrange in ascending order: 0.099, 0.9, 0.89, 0.0999.
5. Round 6.4781 to the nearest hundredth.
6. Which is larger: 5.060 or 5.006?
7. Write 0.375 as a fraction in its simplest form.
8. What is the next number in the sequence: 6.5, 6.45, 6.4, 6.35, ...?
9. How many hundredths are there in 3.5?
10. Which number has the greatest value in the thousandths place: 8.235, 8.325, 8.532, 8.253?

Section B: Addition & Subtraction

11. 15.8 + 4.67 + 0.3 =
12. 20.01 - 3.8 =
13. 7 - 2.345 =
14. 12.4 + 5.08 + 0.9 =
15. 8.5 - 4.67 =
16. 10.1 - 0.99 =
17. 6.7 + 12.35 + 1.002 =
18. 25.4 - 12.75 =
19. 4.2 + 3.05 + 0.8 =
20. 9.06 - 5.7 =

Section C: Multiplying & Dividing

21. 4.5 × 0.8 =
22. 0.6 × 0.07 =
23. 12.5 × 1.2 =
24. 3.24 ÷ 6 =
25. 4.8 ÷ 0.4 =
26. 0.81 ÷ 0.9 =
27. 7.5 × 0.4 =
28. 6.3 ÷ 0.07 =
29. 0.125 × 8 =
30. 5.6 ÷ 0.08 =

Section D: Conversions & Mixed Applications

31. Convert 0.88 to a fraction in its simplest form.
32. Convert 7/8 to a decimal.
33. Convert 0.03 to a percentage.
34. What is 30% of 8.5?
35. Express 19/20 as a decimal.
36. Write 0.075 as a fraction in its simplest form.
37. What is 15% of 4.0?
38. Convert 1.25 to a mixed number.
39. What is 1/5 of 7.5?
40. Convert 0.004 to a percentage.

Section E: Mixed Problem Solving

41. A piece of string is 3.6m long. If I cut off 1.45m, how much is left?
42. One apple costs £0.28. How much do 6 apples cost?
43. A box of 24 pencils costs £7.20. What is the cost per pencil?
44. A car travels 84.5 miles on 6.5 gallons of petrol. How many miles per gallon does it do?
45. The perimeter of a square is 15.6cm. What is the length of one side?
46. A bag of sugar weighs 2.4kg. If I use 0.85kg in a recipe, how much is left?
47. A book has 240 pages. If I have read 0.65 of the book, how many pages have I read?
48. A bottle holds 2.25 litres of water. How many 0.25 litre glasses can be filled from it?
49. A rectangle has a length of 5.2cm and a width of 3.5cm. What is its area?
50. A packet of crisps weighs 0.35kg. How much would 8 packets weigh?

Section F: Mixed Word Problems & Multi-step

51. Tom buys a magazine for £2.85 and a drink for £1.40. He pays with a £5 note. How much change does he get?
52. A piece of rope is 8m long. I cut off 3 pieces each of 1.25m. How much rope is left?
53. A box of 36 chocolates costs £12.60. What is the cost per chocolate?
54. A car uses 0.065 litres of fuel per kilometre. How much fuel is used for a 60km journey?
55. A shop reduces a £60 coat by 20%. What is the new price?
56. A recipe for 6 people requires 0.75kg of flour. How much flour is needed for 10 people?
57. A tank holds 120 litres. It is being filled at a rate of 7.5 litres per minute. How long will it take to fill?
58. A packet of biscuits contains 15 biscuits. Each biscuit weighs 0.032kg. What is the total weight of the packet?
59. A train travels at a constant speed of 90km/h. How far does it travel in 1 hour and 15 minutes?
60. A rectangle has a perimeter of 24.8cm. If its length is 7.5cm, what is its width?
61. A bag of potatoes weighs 5.6kg. I remove 4 potatoes with a combined weight of 1.25kg. What is the new weight of the bag?
62. A bottle of juice contains 1.75 litres. I pour out 0.4 litres. How much juice is left?
63. A book costs £8.50. How many books can I buy with £50?
64. A bus has 52 seats. 0.75 of the seats are occupied. How many seats are empty?
65. A piece of wood is 4.8m long. I need to cut it into 0.3m lengths. How many full pieces can I get?

Section G: Fictional "Previous Year Paper" (50 Questions)

66. Calculate 13.4 + 7.65
67. What is 8.2 - 3.47?
68. Multiply 4.5 by 0.6
69. Divide 10.8 by 0.9
70. Round 7.269 to one decimal place.
71. Which is larger: 3.099 or 3.1?
72. Write 0.625 as a fraction in its simplest form.
73. Convert the fraction 3/5 to a decimal.
74. What is 40% of 6.5?
75. A box of 10 pencils costs £3.50. What is the cost of one pencil?
76. A car travels 72km in 1.2 hours. What is its average speed in km/h?
77. A rectangle measures 4.3cm by 6.2cm. What is its area?
78. A bag of flour weighs 1.5kg. I use 450g. How much flour is left in kilograms?
79. What is the perimeter of a square with a side length of 5.7cm?
80. A train ticket costs £14.75. I buy 2 tickets. How much change do I get from £40?
81. A bottle contains 2 litres of water. I drink 350ml. How much water is left in litres?
82. A cake recipe requires 0.45kg of butter. I want to make 1.5 times the recipe. How much butter do I need?
83. A packet of sweets costs £0.95. I buy 5 packets. How much change from a £10 note?
84. A bus has 48 seats. 5/8 of the seats are occupied. How many seats are empty?
85. A piece of ribbon is 5m long. I cut off 3 pieces, each 0.75m long. How much ribbon is left?
86. A book has 180 pages. I have read 2/3 of the book. How many pages have I read?
87. A box of 12 eggs costs £2.76. What is the cost per egg?
88. A car uses 0.08 litres of fuel for every kilometre. How much fuel is needed for a 250km journey?
89. A shirt costs £28.00. In a sale, it is reduced by 15%. What is the sale price?
90. A triangle has a base of 8cm and a height of 5.5cm. What is its area?
91. A bag of oranges weighs 3.2kg. I take out 3 oranges weighing 0.45kg in total. What is the new weight?
92. A jug contains 1.8 litres of milk. I pour 0.55 litres into a bowl. How much milk remains in the jug?
93. A pen costs £1.45. How many pens can I buy with £20?
94. A cycling race is 30km long. A cyclist has completed 0.7 of the race. How far has she cycled?
95. A plank of wood is 6m long. How many 0.4m lengths can be cut from it?
96. What is the value of the 4 in 19.046?
97. Write the number twelve and nine hundredths as a decimal.
98. Put these in order from smallest to largest: 2.02, 2.2, 2.002, 2.202
99. Calculate 0.1 × 0.1
100. Calculate 1.44 ÷ 1.2
101. Express 17/25 as a percentage.
102. Find 3/8 of 9.6
103. A TV programme starts at 7:35 pm and ends at 8:20 pm. How long does it last in hours?
104. A bag of 20 marbles weighs 0.5kg. What is the weight of one marble in grams?
105. A recipe needs 0.025kg of salt. How much salt is needed for 8 batches?
106. 5.67 × 100 =
107. 34.8 ÷ 1000 =
108. 0.07 × 0.3 =
109. 4.5 + ? = 10
110. ? - 3.75 = 2.8
111. 6.3 ÷ ? = 9
112. ? × 0.4 = 1
113. A digital clock shows 14:25. What time is this in 12-hour format?
114. In a class of 30 children, 18 are girls. What fraction of the class are boys?
115. A bathtub has 120 litres of water. 45 litres are removed. What percentage of the water remains?

Section H: 50 More GL Assessment Styles

116. Calculate: 23.4 - 7.89
117. What is 6.7 × 0.5?
118. Divide 8.4 by 0.07
119. Round 12.3456 to three decimal places.
120. Which number is the smallest: 0.101, 0.011, 0.11, 0.0111?
121. Convert 22/1000 to a decimal.
122. What is 12.5% of £40?
123. A bag of 5 lemons costs £1.10. What is the cost of one lemon?
124. A cube has a side of length 2.5cm. What is its volume?
125. The sum of two numbers is 15.6. One number is 8.9. What is the other number?
126. Write 4.5% as a decimal.
127. A pizza is cut into 8 equal slices. I eat 3 slices. What decimal of the pizza did I eat?
128. A coat costs £85. Its price is increased by 20%. What is the new price?
129. 0.3 + 0.03 + 0.003 =
130. 1 - 0.007 =
131. 2.5 × 40 =
132. 4.8 ÷ 12 =
133. 7.07 ÷ 10 =
134. 0.9 × 1000 =
135. Find the difference between 10 and 6.54.
136. What is the product of 2.5 and 3.2?
137. A triangle has an area of 24cm² and a base of 8cm. What is its height?
138. A pen is 13.5cm long. A pencil is 8.7cm long. How much longer is the pen?
139. A bottle holds 1.5 litres. A glass holds 0.2 litres. How many full glasses can be poured?
140. The temperature was -2°C. It rises by 5°C. What is the new temperature?
141. Which is heavier: 0.25kg or 350g?
142. A field is 40m long and 35.5m wide. What is the perimeter of the field?
143. 3/10 of a number is 9.3. What is the number?
144. A bus leaves at 10:15 am and arrives at 1:05 pm. How long is the journey?
145. A bag has 3 red, 5 blue, and 2 green balls. What is the probability of picking a blue ball?
146. Simplify the ratio 15:20.
147. A map scale is 1:25000. What is the actual distance if the map distance is 4cm?
148. A jacket was £60. It is in a sale with 1/3 off. What is the sale price?
149. 1.5 hours = ____ minutes.
150. 6500g = ____ kg.
151. 2.3km = ____ m.
152. 45mm = ____ cm.
153. 3/4 litre = ____ ml.
154. Find the mean of 4, 7, 5, 9, 5.
155. What is the range of the numbers in Q154?
156. (2.3 + 1.7) × 4 =
157. 5.6 - (2.1 + 0.9) =
158. 10 × (0.5 + 0.05) =
159. A number is multiplied by 10 and then 3 is added. The answer is 43. What was the original number?
160. The coordinates of a point are (3, 5). What are the coordinates after a reflection in the x-axis?
161. How many lines of symmetry does a square have?
162. What is the size of one interior angle of an equilateral triangle?
163. A roll of tape is 15m long. I use 7 pieces, each 0.85m long. How much tape is left?
164. A recipe for 4 people uses 2 eggs. How many eggs are needed for 10 people?
165. A number, when divided by 0.5, gives an answer of 16. What is the number?

Answer Key & Solutions — Sections A–H

Section A

1. 8 hundredths (0.08)

2. 7.024

3. 4.75

4. 0.099, 0.0999, 0.89, 0.9

5. 6.48

6. 5.060

7. 3/8

8. 6.3

9. 350

10. 8.532 (thousandths digit is 2)

Section B

11. 20.77

12. 16.21

13. 4.655

14. 18.38

15. 3.83

16. 9.11

17. 20.052

18. 12.65

19. 8.05

20. 3.36

Section C

21. 3.6

22. 0.042

23. 15

24. 0.54

25. 12

26. 0.9

27. 3.0

28. 90

29. 1.000

30. 70

Section D

31. 22/25

32. 0.875

33. 3%

34. 2.55

35. 0.95

36. 3/40

37. 0.6

38. 1 1/4

39. 1.5

40. 0.4%

Section E

41. 2.15m

42. £1.68

43. £0.30

44. 13 mpg

45. 3.9cm

46. 1.55kg

47. 156 pages

48. 9 glasses

49. 18.2 cm²

50. 2.8kg

Section F

51. £0.75

52. 4.25m

53. £0.35

54. 3.9 litres

55. £48

56. 1.25kg

57. 16 minutes

58. 0.48kg

59. 112.5km

60. 4.9cm

61. 4.35kg

62. 1.35 litres

63. 5 books

64. 13 seats

65. 16 pieces

Section G (66–115)

66. 21.05 67. 4.73 68. 2.7 69. 12 70. 7.3 71. 3.1 72. 5/8 73. 0.6 74. 2.6 75. £0.35 76. 60 km/h 77. 26.66 cm² 78. 1.05kg 79. 22.8cm 80. £10.50 81. 1.65 litres 82. 0.675kg 83. £5.25 84. 18 seats 85. 2.75m 86. 120 pages 87. £0.23 88. 20 litres 89. £23.80 90. 22 cm² 91. 2.75kg 92. 1.25 litres 93. 13 pens 94. 21km 95. 15 lengths 96. 4 hundredths 97. 12.09 98. 2.002, 2.02, 2.2, 2.202 99. 0.01 100. 1.2 101. 68% 102. 3.6 103. 0.75 hours (45 mins) 104. 25g 105. 0.2kg 106. 567 107. 0.0348 108. 0.021 109. 4.5 110. 6.55 111. 0.7 112. 2.5 113. 2:25 pm 114. 2/5 115. 62.5%

Section H (116–165)

116. 15.51 117. 3.35 118. 120 119. 12.346 120. 0.011 121. 0.022 122. £5 123. £0.22 124. 15.625 cm³ 125. 6.7 126. 0.045 127. 0.375 128. £102 129. 0.333 130. 0.993 131. 100 132. 0.4 133. 0.707 134. 900 135. 3.46 136. 8.0 137. 6cm 138. 4.8cm 139. 7 glasses 140. 3°C 141. 350g 142. 151m 143. 31 144. 2h 50m 145. 1/2 146. 3:4 147. 1km 148. £40 149. 90 150. 6.5 151. 2300 152. 4.5 153. 750 154. 6 155. 5 156. 16 157. 2.6 158. 5.5 159. 4 160. (3, -5) 161. 4 162. 60° 163. 9.05m 164. 5 eggs 165. 8

Money, Length & Weight Problems (with Solutions)

Money Problems

Q1. £1.25 × 4 = £5.00

Q2. £10.00 - £7.80 = £2.20

Q3. £12.45 × 3 = £37.35

Q4. 35p = £0.35

Q5. £6.50 × 5 = £32.50

Q6. £2.75 + £1.20 = £3.95

Q7. £14.60 × 2 = £29.20

Q8. £9.99 - £7.50 = £2.49

Q9. £3.45 × 10 = £34.50

Q10. £20.00 - £13.85 = £6.15

Q5 (word). £2.45 × 4 = £9.80

Length Problems

Q1. 2.35 + 1.80 = 4.15 m

Q2. 12.40 - 3.75 = 8.65 m

Q3. 1.25 × 100 = 125 cm

Q4. 24.3 - 18.6 = 5.7 cm

Q5. 3.45 + 2.60 = 6.05 km

Q6. 2.75 ÷ 0.5 = 5.5 → 5 pieces

Q7. 1.38 × 1000 = 1380 mm

Q8. 1.25 + 1.75 = 3.00 km

Q9. 4.05 - 3.85 = 0.20 m

Q10. 0.95 + 0.65 = 1.60 m

Weight Problems

Q1. 1.25 × 4 = 5.00 kg

Q2. 2.80 + 1.35 = 4.15 kg

Q3. 750 ÷ 1000 = 0.75 kg

Q4. 3.45 - 2.60 = 0.85 kg

Q5. 12.50 - 4.75 = 7.75 kg

Q6. 23.40 - 4.85 = 18.55 kg

Q7. 1.205 × 1000 = 1205 g

Q8. 7.05 ÷ 2.35 = 3 boxes

Q9. 185 ÷ 1000 = 0.185 kg

Q10. 1.65 + 3.80 = 5.45 kg

Key Tips for Decimal Problems

1. Line up decimal points when adding or subtracting.

2. Check units — convert all measurements to the same unit before calculating.

3. Money calculations — always include two decimal places for pounds.

4. Division — if dividing by a decimal, multiply both numbers to make the divisor a whole number.

5. Real-life context — consider whether the answer needs to be a whole number (e.g., pieces of wood).

Decimals chapter concept of 11 plus exam GL assessment examination