1.9: Exercises

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Analysis

1. Round the following to four significant digits:

a) 14.5423

b) 30056

c) 76.90032

d) 0.00084754

2. Round the following to three significant digits:

a) 354.005

b) 9100.46

c) 1.0054

d) 0.000052753

3. Round the following to five significant digits:

a) 5.100237

b) 1020.765

c) 1.00540

d) 0.00004578053

4. Round the following to four significant digits:

a) 5.100237

b) 1020.765

c) 1.00540

d) 0.00004578053

5. Convert the following to scientific notation:

a) 23.61

b) 12000

c) 7632

d) 0.00509

6. Convert the following to scientific notation:

a) 4253

b) 640000000

c) 2.03

d) 0.00000658

7. Convert the following to scientific notation:

a) 41.56

b) 954000

c) 84.035

d) 0.0001632

8. Convert the following to scientific notation:

a) 11200

b) 30000000

c) 325.2

d) 0.00002504

9. Convert the following to engineering notation:

a) 12000

b) 470

c) 6.5

d) 0.00198

10. Convert the following to engineering notation:

a) 3500

b) 17.9

c) 5601000

d) 0.0000355

11. Convert the following to engineering notation:

a) 33.2

b) 313.6

c) 43000

d) 0.000076

12. Convert the following to engineering notation:

a) 0.23

b) 76.95

c) 45500

d) 0.00890

For problems 13 through 18 express the results using engineering notation without rounding or truncating.

13. Compute the following:

a) 1.2E2 times 3.0E4

b) 5.4 times 3.1E3

c) 6.01E3 times 2.0E−1

d) 5.3E9 times 4.1E−5

14. Compute the following:

a) 7.1E1 times 4.0E2

b) 2.32 times 5.6E3

c) 6.01E3 times 3.0E−2

d) 5.2E5 times 8.2E−7

15. Compute the following:

a) 8.2E1 / 4E2

b) 2.42 / 2.0E3

c) 6.09E3 / 3.0E−2

d) 9.6E5 / 3.1E−7

16. Compute the following:

a) 4.6E2 / 2.0E2

b) 2.35 / 4.0E6

c) 5.15E4 / 3.0E−3

d) 6.8E−2 / 5.0E−4

17. Compute the following:

a) 8.2E1 + 4E2

b) 2.42 + 2.0E1

c) 6.09E3 − 3.0E−2

d) 9.6E5 − 5.1E6

18. Compute the following:

a) 4.2E3 + 9E2

b) 3.53 + 4.2E−1

c) 1.05E−2 − 5.0E−2

d) 9.4E5 − 3.2E4

For problems 18 through 22 express the results using engineering notation with proper rounding to reflect the resulting resolution.

19. Compute the following:

a) 16.2 − 0.4

b) 4356 + 378

c) 0.012 − 0.005

20. Compute the following:

a) 4.5 \(\cdot\) 43.1

b) 1201 / 23.6

c) 890.1 \(\cdot\) 0.172

21. Compute the following:

a) 51E3 \(\cdot\) 62.7E2

b) 6.733E2 / 1.01E−3

c) 20.12E6 / 65.6E9

22. Compute the following:

a) 17.9E3 − 10.4E6

b) 81E3 + 12E3

c) 76.0E3 + 1465

For problems 23 through 26 determine the result of the computation in SI base units (meters, kilograms, seconds) with appropriate engineering notation units (kilo, milli, etc.).

23. Determine the result of 20 meters times 0.10 kilograms in kg·m.

24. Determine the result of 34 kilometers divided by 10 millimeters.

25. Determine the resulting velocity in m/s if a distance of 3.6 meters is covered in the space of 1.2 milliseconds.

26. Determine the result of 24 \(\mu\)s divided by 3.0 km.