Primary 4 Mathematics · Chapter 9 · Answers and explanations
Chapter 9 Revision Paper: Decimals (answers)
Section A · Multiple choice 10 marks
1. The number line shows 10 equal parts between 6 and 7. Which decimal does the arrow point to?1 mark
(A) 6.03(B) 6.7(C) 6.3(D) 7.3
Answer: (C) 6.3The distance from 6 to 7 is split into 10 equal parts, so each part is 1 tenth (0.1). The arrow is at the 3rd mark after 6, so it shows 6 and 3 tenths = 6.3.
2. What is the value of the digit 6 in 12.964?1 mark
(A) 0.6(B) 0.006(C) 6(D) 0.06
Answer: (D) 0.06Write the places after the decimal point: 9 is in the tenths, 6 is in the hundredths, 4 is in the thousandths. So 6 hundredths = 0.06.
3. Which decimal is the same as 6 ones and 4 hundredths?1 mark
(A) 6.04(B) 6.4(C) 6.004(D) 64
Answer: (A) 6.046 ones is 6. 4 hundredths is 0.04. There are 0 tenths, so write 0 in the tenths place: 6 + 0.04 = 6.04.
4. Which decimal is the same as 8 + 0.03 + 0.004?1 mark
(A) 8.34(B) 8.034(C) 8.304(D) 8.0034
Answer: (B) 8.034Write each part in its place: 8 ones, 0 tenths, 3 hundredths, 4 thousandths. So the number is 8.034.
5. Which of these is NOT equal to 2.5?1 mark
(A) 2.50(B) 2.500(C) 2.05(D) 2 12
Answer: (C) 2.052.5 = 2.50 = 2.500, because a zero at the end of a decimal does not change its value. Also 2 12 = 2.5. But 2.05 has 0 tenths and 5 hundredths, so it is smaller than 2.5.
6. Which is the greatest?1 mark
(A) 4.09(B) 4.19(C) 4.091(D) 4.9
Answer: (D) 4.9All four have 4 ones. Now compare the tenths: 0, 9, 1, 0. The greatest tenths digit is 9, so 4.9 is the greatest. A longer decimal is not always a greater one.
7. Which list shows the decimals in order, from the smallest to the greatest?1 mark
(A) 0.508, 0.58, 0.8, 0.85(B) 0.508, 0.58, 0.85, 0.8(C) 0.58, 0.508, 0.8, 0.85(D) 0.85, 0.8, 0.58, 0.508
Answer: (A) 0.508, 0.58, 0.8, 0.85Compare the tenths: 5, 5, 8, 8. For the two with 5 tenths, compare hundredths: 0.508 has 0 and 0.58 has 8, so 0.508 < 0.58. For the two with 8 tenths, 0.8 = 0.80 < 0.85. The order is 0.508, 0.58, 0.8, 0.85.
8. What is the next number in the pattern? 7.45, 7.40, 7.35, 7.30, ____1 mark
(A) 7.20(B) 7.25(C) 7.29(D) 7.15
Answer: (B) 7.25Each number is 0.05 less than the one before it: 7.45 − 0.05 = 7.40, and so on. So the next number is 7.30 − 0.05 = 7.25.
9. Round 3.846 to 2 decimal places.1 mark
(A) 3.84(B) 3.8(C) 3.85(D) 3.9
Answer: (C) 3.85Keep 2 decimal places: 3.84. Look at the thousandths digit, which is 6. Since 6 is 5 or more, round the hundredths up: 3.84 becomes 3.85.
10. Express 0.45 as a fraction in its simplest form.1 mark
(A) 45100(B) 9100(C) 45(D) 920
Answer: (D) 9200.45 = 45100. Divide the top and bottom by 5: 920. It cannot be simplified any further.
Section B · Short answers 4 marks
11. Round 4.396 to 1 decimal place.1 mark
Answer: 4.4Keep 1 decimal place: 4.3. The hundredths digit is 9, which is 5 or more, so round the tenths up: 4.4.
12. Express 725 as a decimal.1 mark
Answer: 0.28Make the bottom number 100: 725 = 7 × 425 × 4 = 28100. 28 hundredths = 0.28.
13. Express 3.6 as a mixed number in its simplest form.1 mark
Answer: 3 353.6 = 3 and 6 tenths = 3 610. Divide the top and bottom of the fraction by 2: 3 35.
14. Find the missing number in the pattern. 1.20, 1.35, 1.50, ____, 1.801 mark
Answer: 1.65Each number is 0.15 more than the one before: 1.20 + 0.15 = 1.35, 1.35 + 0.15 = 1.50. So 1.50 + 0.15 = 1.65. Check: 1.65 + 0.15 = 1.80.
Section C · Show your working 16 marks
15. A string has 100 beads. 6 beads are red and 30 beads are blue.
(a) Express the fraction of red beads as a decimal.
(b) Express the fraction of blue beads as a decimal.2 marks
Answer: (a) 0.06 (b) 0.3(a) Red beads: 6100. 6 hundredths = 0.06.
(b) Blue beads: 30100 = 310. 3 tenths = 0.3 (the same as 0.30).
16. A decimal has 3 in the ones place, 0 in the tenths place, 8 in the hundredths place and 5 in the thousandths place.
(a) Write the decimal.
(b) What is the value of the digit 8?2 marks
Answer: (a) 3.085 (b) 0.08(a) Put each digit in its place: 3 ones, 0 tenths, 8 hundredths, 5 thousandths = 3.085. The 0 holds the tenths place.
(b) The 8 is in the hundredths place, so its value is 8 hundredths = 0.08.
17. Arrange these decimals in order, from the greatest to the smallest.
2.4, 2.04, 2.404, 2.442 marks
Answer: 2.44, 2.404, 2.4, 2.04All have 2 ones. Tenths: 4, 0, 4, 4, so 2.04 is the smallest. For the other three, compare hundredths: 2.4 = 2.400 has 0, 2.404 has 0, 2.44 has 4. So 2.44 is the greatest. Then compare 2.404 and 2.400: thousandths 4 and 0, so 2.404 > 2.4. Order: 2.44, 2.404, 2.4, 2.04.
18. Look at the number pattern: 0.90, 1.15, 1.40, 1.65, ...
(a) What is the rule?
(b) What is the 6th number in the pattern?2 marks
Answer: (a) Add 0.25 (b) 2.15(a) 1.15 − 0.90 = 0.25, and 1.40 − 1.15 = 0.25, so the rule is add 0.25.
(b) 5th number: 1.65 + 0.25 = 1.90. 6th number: 1.90 + 0.25 = 2.15.
19. A rope is 7.96 m long.
(a) Round its length to 1 decimal place.
(b) Round its length to the nearest whole number.2 marks
Answer: (a) 8.0 m (b) 8 m(a) Keep 1 decimal place: 7.9. The hundredths digit is 6, so round up: 7.9 becomes 8.0. Keep the 0 to show 1 decimal place.
(b) The tenths digit is 9, so round the ones up: 8 m.
20. A pail holds 2.45 ℓ of water. Express this amount as a mixed number of litres in its simplest form.2 marks
Answer: 2 920 ℓ2.45 = 2 and 45 hundredths = 2 45100. Divide the top and bottom of the fraction by 5: 45 ÷ 5100 ÷ 5 = 920. So the amount is 2 920 ℓ.
21. A number with 2 decimal places is rounded to 1 decimal place and the answer is 5.3. What are the smallest and the greatest numbers it could be?2 marks
Answer: Smallest 5.25; greatest 5.34Numbers that round to 5.3 lie between 5.25 and 5.35, but 5.35 itself rounds up to 5.4. The smallest is 5.25: its hundredths digit is 5, so it rounds up to 5.3. The greatest 2-decimal-place number below 5.35 is 5.34: its hundredths digit is 4, so it rounds down to 5.3.
22. Mei has three ribbons. The red ribbon is 2.35 m long, the blue ribbon is 2 925 m long and the green ribbon is 2.4 m long. Arrange the ribbons in order, from the shortest to the longest.2 marks
Answer: Red, blue, greenChange 2 925 to a decimal: 925 = 9 × 425 × 4 = 36100 = 0.36, so the blue ribbon is 2.36 m. Write the green ribbon as 2.40 m. All have 2 ones and 3 or 4 tenths: 2.35 (3 tenths), 2.36 (3 tenths), 2.40 (4 tenths). 2.40 is the longest. 2.35 < 2.36 because 5 hundredths < 6 hundredths. From the shortest: red (2.35 m), blue (2.36 m), green (2.4 m).
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