ROUNDING TO SIGNIFICANT FIGURES WORKSHEET

1. Three different people measure the length of a room. The measurements given by them are 7.8 meters, 8 meters and 7.76 meters. Which is the most appropriate measurement ?

2. Round 6.7845 to 3 significant figures.

3. Round 0.0360578 to 4 significant figures.

4. Round 10.86 to 2 significant figures.

5. Evaluate the following multiplication and round your answer to the approximate number of significant digits.

8.0000 x 0.004

6. Evaluate the following division and round your answer to the approximate number of significant digits.

30,000 ÷ 3.004

7. Evaluate the following multiplication and round your answer to the approximate number of significant digits.

6.14 x 30.5 x 500

8. Evaluate the following division and round your answer to the approximate number of significant digits.

0.009 ÷ 7

9. Using the approximation 1 in. = 2.54 cm, convert 24.25 inches to centimeters.

10. Using the approximation 1 kg = 2.2 pounds, convert 125 pounds to kilograms.

11. Evaluate :

3.78 + 2.7 + 4.203

12. Evaluate :

2.56 - 1.235

Answers

1. Answer :

This can be determined by the number of “significant figures”, in the measurement.

7.8 meters has 2 significant figures

8 meters has 1 significant figure

7.76 meters has 3 significant figures

The measurement of 7.76 meters is more precise than 7.8 meters or 8 meters because it has more significant digits.

2. Answer :

All the digits in 6.7845 are non-zero digits.

6.7845 has 5 significant figures

If you want to round 6.7845 to 3 significant figures, look at the digit after the third significant figure.

In 6.7845, the digit after the third significant figure is 4.

6.7845

Since the digit after the third significant figure is 4, keep the previous digit 8 same.

6.7845 to 3 significant figures = 6.78

3. Answer :

0.0360578 has 6 significant figures

If you want to round 0.0360578 to 4 significant figures, look at the digit after the fourth significant figure.

In 0.0360578, the digit after the fourth significant figure is 7.

0.0360578

Since the digit after the fourth significant figure is 7, increase the previous digit 5 by 1.

0.0360578 to 4 significant figures = 0.03606

4. Answer :

10.86 has 4 significant figures

If you want to round 10.86 to 2 significant figures, look at the digit after the second significant figure.

In 10.86, the digit after the second significant figure is 8.

10.86

Since the digit after the second significant figure is 8, increase the previous digit 0 by 1.

10.86 to 2 significant figures = 11

5. Answer :

8.0000 x 0.004 = 0.032 

8.0000 has 5 significant figures

0.004 has 1 significant figure

We have the least number of significant figures in 0.004, that is 1 significant figure.

So the final answer will have 1 significant figure.

Final answer : 0.03

6. Answer :

30,000 ÷ 3.004 = 9986.68442.........

30,000 has 5 significant figures

3.004 has 4 significant figures

We have the least number of significant figures in 3.004, that is 4 significant figures.

So the final answer will have 4 significant figures.

Final answer : 9987

7. Answer :

6.14 x 30.5 x 500 = 93,635

6.14 has 3 significant figures

30.5 has 3 significant figures

500 has 3 significant figures

In all the three numbers, we have the number of significant figures, that is 3 significant figures.

So the final answer will have 3 significant figures.

Final answer : 93,600

8. Answer :

0.009 ÷ 7 = 0.012857.........

0.009 has 1 significant figure

7 has 1 significant figure

In both the numbers, we have the same number of significant figures, that is 1 significant figure.

So the final answer will have 1 significant figure.

Final answer : 0.001

9. Answer :

24.25 x 2.54 = 61.595 

24.25 has 4 significant figures

2.54 has 3 significant figures

We have the least number of significant figures in 2.54, that is 3 significant figures.

So the final answer will have 3 significant figures.

Final answer : 61.6 centimeters.

10. Answer :

125 ÷ 2.2 = 56.818181......... 

125 has 3 significant figures

2.2 has 2 significant figures

We have the least number of significant figures in 2.2, that is 2 significant figures.

So the final answer will have 2 significant figures, making it no more precise than the least precise.

Final answer : 57 kilograms.

11. Answer :

3.78 + 2.7 + 4.203 = 10.683

3.78 has 2 decimal places.

2.7 has 1 decimal place.

4.203 has 3 decimal places.

The fewest decimal places is 1.

The final answer is 10.7.

12. Answer :

2.56 - 1.235 = 1.325

2.56 has 2 decimal places.

1.325 has 3 decimal places.

The fewest decimal places is 2.

The final answer is 1.33.

Note :

It is not necessary to count the number of significant figures when doing addition or subtraction.

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