7. Arrange from the smallest to the greatest: 2.709, 2.97, 2.79.2 marks
Answer: 2.709, 2.79, 2.97Tenths: 7, 9, 7. So 2.97 is the greatest. For the other two, hundredths: 0 and 9.
8. Arrange from the greatest to the smallest: 0.3, 0.33, 0.303.2 marks
Answer: 0.33, 0.303, 0.3Tenths are all 3. Hundredths: 0, 3, 0. 0.33 is greatest; then compare 0.303 and 0.3 (0.300).
9. Find the missing number: 1.2, 1.3, 1.4, ____, 1.6.1 mark
Answer: 1.5The rule is add 0.1.
10. Find the missing number: 3.40, 3.45, 3.50, ____, 3.60.1 mark
Answer: 3.55The rule is add 0.05.
11. What is the rule? 8.0, 7.5, 7.0, 6.5.1 mark
Answer: Subtract 0.5Each number is 0.5 less than the one before.
12. Tara says 0.45 is greater than 0.5 because 45 is greater than 5. Is she right? Explain.2 marks
Answer: No. 0.5 is greater0.5 = 0.50 and 0.50 > 0.45. Compare place by place, not by the number of digits.
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Primary 4 Mathematics · Chapter 9 · Answers and explanations
Lesson 9.5: Rounding Decimals (answers)
Section A · Multiple choice 4 marks
1. Round 4.7 to the nearest whole number.1 mark
(A) 4(B) 5(C) 4.5(D) 7
Answer: (B) 5The tenths digit is 7 (5 or more), so round up to 5.
2. Round 12.3 to the nearest whole number.1 mark
(A) 12(B) 13(C) 12.5(D) 10
Answer: (A) 12The tenths digit is 3 (less than 5), so round down to 12.
3. Round 6.48 to 1 decimal place.1 mark
(A) 6.4(B) 6.5(C) 6.6(D) 6.0
Answer: (B) 6.5The hundredths digit is 8, so round the tenths up: 6.5.
4. Which number does NOT round to 3.6 when rounded to 1 decimal place?1 mark
(A) 3.55(B) 3.58(C) 3.66(D) 3.64
Answer: (C) 3.663.66 has 6 hundredths, so it rounds up to 3.7. The others round to 3.6.
Section B · Write your answer 10 marks
5. Round 8.5 to the nearest whole number.1 mark
Answer: 9The tenths digit is 5, so round up.
6. Round 0.934 to 1 decimal place.1 mark
Answer: 0.9The hundredths digit is 3, so keep 0.9.
7. Round 7.995 to 2 decimal places.1 mark
Answer: 8.00The thousandths digit is 5, so round up: 7.99 becomes 8.00.
8. Round 15.62 to the nearest whole number.1 mark
Answer: 16The tenths digit is 6, so round up.
9. Round 2.149 to 2 decimal places.1 mark
Answer: 2.15The thousandths digit is 9, so round the hundredths up.
10. A ribbon is 3.46 m long. Round its length to 1 decimal place. 1 mark
Answer: 3.5 mThe hundredths digit is 6, so round up to 3.5 m.
11. Name the smallest and the greatest 2-decimal-place number that rounds to 5.3 when rounded to 1 decimal place.2 marks
Answer: 5.25 and 5.34Numbers from 5.25 up to 5.34 round to 5.3.
12. Sam rounds 6.45 to 1 decimal place and gets 6.4. Is he right? Explain.2 marks
Answer: No. It is 6.5The hundredths digit is 5, so round up to 6.5.
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Primary 4 Mathematics · Chapter 9 · Answers and explanations
Lesson 9.6: Fractions and Decimals (answers)
Section A · Multiple choice 4 marks
1. Express 310 as a decimal.1 mark
(A) 0.03(B) 0.3(C) 3.0(D) 30
Answer: (B) 0.33 tenths = 0.3.
2. Express 34 as a decimal.1 mark
(A) 0.34(B) 0.75(C) 0.7(D) 0.43
Answer: (B) 0.753/4 = 75/100 = 0.75.
3. Express 0.6 as a fraction in its simplest form.1 mark
(A) 610(B) 35(C) 23(D) 16
Answer: (B) 350.6 = 6/10. Divide the top and bottom by 2 to get 3/5.
4. Express 1.25 as a mixed number in its simplest form.1 mark
(A) 1 25100(B) 1 14(C) 1 15(D) 1 52
Answer: (B) 1 141.25 = 1 + 25/100 = 1 + 1/4.
Section B · Write your answer 11 marks
5. Express 7100 as a decimal.1 mark
Answer: 0.077 hundredths = 0.07.
6. Express 12 as a decimal.1 mark
Answer: 0.51/2 = 5/10 = 0.5.
7. Express 920 as a decimal.1 mark
Answer: 0.45Multiply the top and bottom by 5: 9/20 = 45/100 = 0.45.
8. Express 2 15 as a decimal.1 mark
Answer: 2.21/5 = 2/10, so 2 + 0.2 = 2.2.
9. Express 0.35 as a fraction in its simplest form.2 marks
Answer: 7200.35 = 35/100. Divide the top and bottom by 5 to get 7/20.
10. Express 0.09 as a fraction.1 mark
Answer: 91009 hundredths = 9/100.
11. Express 4.8 as a mixed number in its simplest form.2 marks
Answer: 4 454.8 = 4 + 8/10 = 4 + 4/5.
12. Raj ate 0.75 of a pizza. What fraction of the pizza is that, in its simplest form?2 marks
Answer: 340.75 = 75/100. Divide the top and bottom by 25 to get 3/4.
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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
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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