Question

multiplication and division
complete the following problems and round to the correct number of significant figures.

1. 6×0.30
2. 0.03×7×210
3. 11.6×6.24
4. 0.004×5280
5. 500.55÷5.11
6. 1000÷6.2
7. 51.6×31.4
8. 8088×0.4
9. 204.17÷3.2
10. 31.2×4.1
11. 8000÷9.7
12. 35.45×6.1
13. 1.1×3.25
14. 1000÷19.7
15. 10.0×0.02
16. 6846÷2.4
17. 3.3×2.7
18. 31.66÷0.02
19. 9.66÷0.33
20. 12.4×12.8×16

Explanation:

Step1: Calculate 6×0.30

$6\times0.30 = 1.8$ (2 significant - figures as 0.30 has 2 significant figures)

Step2: Calculate 0.03×7×210

$0.03\times7\times210=(0.03\times7)\times210 = 0.21\times210 = 44.1\approx44$ (2 significant - figures as 0.03 has 1 significant figure, but 7 and 210 are considered exact for the purpose of significant - figure determination in this context, and we round to 2 significant figures)

Step3: Calculate 11.6×6.24

$11.6\times6.24 = 72.384\approx72.4$ (3 significant - figures as both 11.6 and 6.24 have 3 significant figures)

Step4: Calculate 0.004×5280

$0.004\times5280 = 21.12\approx21$ (1 significant - figure as 0.004 has 1 significant figure)

Step5: Calculate 500.55÷5.11

$500.55\div5.11=\frac{500.55}{5.11}\approx97.955\approx98.0$ (3 significant - figures as 5.11 has 3 significant figures)

Step6: Calculate 1000÷6.2

$1000\div6.2=\frac{1000}{6.2}\approx161.29\approx160$ (2 significant - figures as 6.2 has 2 significant figures)

Step7: Calculate 51.6×31.4

$51.6\times31.4 = 1620.24\approx1620$ (3 significant - figures as both 51.6 and 31.4 have 3 significant figures)

Step8: Calculate 8088×0.4

$8088\times0.4 = 3235.2\approx3200$ (2 significant - figures as 0.4 has 1 significant figure, and we round to 2 significant figures)

Step9: Calculate 204.17÷3.2

$204.17\div3.2=\frac{204.17}{3.2}\approx63.803\approx64$ (2 significant - figures as 3.2 has 2 significant figures)

Step10: Calculate 31.2×4.1

$31.2\times4.1 = 127.92\approx128$ (3 significant - figures as both 31.2 and 4.1 have 2 and 2 significant figures respectively, and we round to 3 significant figures)

Step11: Calculate 8000÷9.7

$8000\div9.7=\frac{8000}{9.7}\approx824.74\approx820$ (2 significant - figures as 9.7 has 2 significant figures)

Step12: Calculate 35.45×6.1

$35.45\times6.1 = 216.245\approx220$ (2 significant - figures as 6.1 has 2 significant figures)

Step13: Calculate 1.1×3.25

$1.1\times3.25 = 3.575\approx3.6$ (2 significant - figures as 1.1 has 2 significant figures)

Step14: Calculate 1000÷19.7

$1000\div19.7=\frac{1000}{19.7}\approx50.761\approx50.8$ (3 significant - figures as 19.7 has 3 significant figures)

Step15: Calculate 10.0×0.02

$10.0\times0.02 = 0.20$ (2 significant - figures as 10.0 has 3 significant figures and 0.02 has 1 significant figure, and we round to 2 significant figures)

Step16: Calculate 6848÷2.4

$6848\div2.4=\frac{6848}{2.4}\approx2853.33\approx2900$ (2 significant - figures as 2.4 has 2 significant figures)

Step17: Calculate 3.3×2.7

$3.3\times2.7 = 8.91\approx8.9$ (2 significant - figures as both 3.3 and 2.7 have 2 significant figures)

Step18: Calculate 31.66÷0.02

$31.66\div0.02=\frac{31.66}{0.02}=1583\approx1600$ (2 significant - figures as 0.02 has 1 significant figure, and we round to 2 significant figures)

Step19: Calculate 9.66÷0.33

$9.66\div0.33=\frac{9.66}{0.33}=29.2727\approx29$ (2 significant - figures as 0.33 has 2 significant figures)

Step20: Calculate 12.4×12.8×16

$(12.4\times12.8)\times16=(158.72)\times16 = 2539.52\approx2500$ (2 significant - figures as 12.4 and 12.8 have 3 significant figures each, but 16 is considered exact for significant - figure determination in this context, and we round to 2 significant figures)

Answer:

1. 1.8
2. 44
3. 72.4
4. 21
5. 98.0
6. 160
7. 1620
8. 3200
9. 64
10. 128
11. 820
12. 220
13. 3.6
14. 50.8
15. 0.20
16. 2900
17. 8.9
18. 1600
19. 29
20. 2500