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significant figures multiplication and division complete the following …

Question

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

  1. 6 x 0.30
  2. 0.03 x 7 x 210
  3. 11.6 x 6.24
  4. 0.004 x 5280
  5. 500.55 ÷ 5.11
  6. 1000 ÷ 8.2
  7. 51.6 x 31.4
  8. 8088 x 0.4
  9. 204.17 ÷ 3.2
  10. 31.2 x 4.1
  11. 8000 ÷ 9.7
  12. 35.45 x 6.1
  13. 1.1 x 3.25
  14. 1000 ÷ 19.7
  15. 10.0 x 0.02
  16. 6848 ÷ 2.4
  17. 3.3 x 2.7
  18. 31.66 ÷ 0.02
  19. 9.66 ÷ 0.33
  20. 12.4 x 12.8 x 16

Explanation:

Step1: Recall significant - figure rules

For multiplication and division, the result should have the same number of significant figures as the number with the fewest significant figures in the values being multiplied or divided.

Step2: Solve 6×0.30

$6$ has 1 significant - figure, $0.30$ has 2 significant - figures. $6\times0.30 = 1.8$. Rounding to 1 significant - figure gives 2.

Step3: Solve 0.03×7×210

$0.03$ has 1 significant - figure, $7$ has 1 significant - figure, $210$ has 2 significant - figures. $0.03\times7\times210=44.1$. Rounding to 1 significant - figure gives 40.

Step4: Solve 11.6×6.24

$11.6$ has 3 significant - figures, $6.24$ has 3 significant - figures. $11.6\times6.24 = 72.384$. Rounding to 3 significant - figures gives 72.4.

Step5: Solve 0.004×5280

$0.004$ has 1 significant - figure, $5280$ has 3 significant - figures. $0.004\times5280 = 21.12$. Rounding to 1 significant - figure gives 20.

Step6: Solve 500.55÷5.11

$500.55$ has 5 significant - figures, $5.11$ has 3 significant - figures. $500.55\div5.11\approx97.955$. Rounding to 3 significant - figures gives 98.0.

Step7: Solve 1000÷8.2

$1000$ (exact value in some contexts, but here assume 1 significant - figure as no decimal point), $8.2$ has 2 significant - figures. $1000\div8.2\approx121.95$. Rounding to 1 significant - figure gives 100.

Step8: Solve 51.6×31.4

$51.6$ has 3 significant - figures, $31.4$ has 3 significant - figures. $51.6\times31.4 = 1620.24$. Rounding to 3 significant - figures gives 1620.

Step9: Solve 8088×0.4

$8088$ has 4 significant - figures, $0.4$ has 1 significant - figure. $8088\times0.4 = 3235.2$. Rounding to 1 significant - figure gives 3000.

Step10: Solve 204.17÷3.2

$204.17$ has 5 significant - figures, $3.2$ has 2 significant - figures. $204.17\div3.2\approx63.803$. Rounding to 2 significant - figures gives 64.

Step11: Solve 31.2×4.1

$31.2$ has 3 significant - figures, $4.1$ has 2 significant - figures. $31.2\times4.1 = 127.92$. Rounding to 2 significant - figures gives 130.

Step12: Solve 8000÷9.7

$8000$ (assume 1 significant - figure), $9.7$ has 2 significant - figures. $8000\div9.7\approx824.74$. Rounding to 1 significant - figure gives 800.

Step13: Solve 35.45×6.1

$35.45$ has 4 significant - figures, $6.1$ has 2 significant - figures. $35.45\times6.1 = 216.245$. Rounding to 2 significant - figures gives 220.

Step14: Solve 1.1×3.25

$1.1$ has 2 significant - figures, $3.25$ has 3 significant - figures. $1.1\times3.25 = 3.575$. Rounding to 2 significant - figures gives 3.6.

Step15: Solve 1000÷19.7

$1000$ (assume 1 significant - figure), $19.7$ has 3 significant - figures. $1000\div19.7\approx50.761$. Rounding to 1 significant - figure gives 50.

Step16: Solve 10.0×0.02

$10.0$ has 3 significant - figures, $0.02$ has 1 significant - figure. $10.0\times0.02 = 0.2$. Rounding to 1 significant - figure gives 0.2.

Step17: Solve 6848÷2.4

$6848$ has 4 significant - figures, $2.4$ has 2 significant - figures. $6848\div2.4\approx2853.33$. Rounding to 2 significant - figures gives 2900.

Step18: Solve 3.3×2.7

$3.3$ has 2 significant - figures, $2.7$ has 2 significant - figures. $3.3\times2.7 = 8.91$. Rounding to 2 significant - figures gives 8.9.

Step19: Solve 31.66÷0.02

$31.66$ has 4 significant - figures, $0.02$ has 1 significant - figure. $31.66\div0.02 = 1583$. Rounding to 1 significant - figure gives 2000.

Step20: Solve 9.66÷0.33

$9.66$ has 3 significant - figures, $0.33$ has 2 significant - figures. $9.66\div0.33 = 29.2727\cdots$. Rounding to 2 significant - figures gives 29.

Step21:…

Answer:

  1. 2
  2. 40
  3. 72.4
  4. 20
  5. 98.0
  6. 100
  7. 1620
  8. 3000
  9. 64
  10. 130
  11. 800
  12. 220
  13. 3.6
  14. 50
  15. 0.2
  16. 2900
  17. 8.9
  18. 2000
  19. 29
  20. 2500