# Exercises: More Unit Conversions and Rounding Rules (2.4)

## Exercises: Significant Figures

Instructions: For questions 1–22, ensure that your answers have the appropriate number of significant figures according to our rules for precision and accuracy.

1. Write the two conversion factors that exist between the two given units.

a. millilitres and litres
b. microseconds and seconds
c. kilometres and meters

Solution

a. $1\text{,}000\text{ mL}/1\text{ L}$ and $1\text{ L}/1\text{,}000\text{ mL}$
b. $1\text{,}000\text{,}000\text{ μs}/1\text{ s}$ and $1\text{ s}/1\text{,}000\text{,}000\text{ μs}$
c. $1\text{,}000\text{ m}/1\text{ km}$ and $1\text{ km}/1\text{,}000\text{ m}$

2. Write the two conversion factors that exist between the two given units.

a. kilograms and grams
b. milliseconds and seconds
c. centimetres and meters

3. Perform the following conversions.

a. $5.4$ km to meters
b. $0.665$ m to millimetres
c. $0.665$ m to kilometres

Solution

a. $5\text{,}400$ m
b. $665$ mm
c. $6.65\times10^{−4}$ km

4. Perform the following conversions.

a. $90.6$ mL to litres
b. $0.00066$ mL to litres
c. $750$ L to kilolitres

5. Perform the following conversions.

a. $17.8$ μg to grams
b. $7.22\times10^2$ kg to grams
c. $0.00118$ g to nanograms

Solution

a. $1.78\times10^{−5}$ g
b. $7.22\times10^5$ g
c. $1.18\times10^6$ ng

6. Perform the following conversions.

a. $833$ ns to seconds
b. $5.809$ s to milliseconds
c. $2.77\times10^6$ s to megaseconds

7. Perform the following conversions.

a. $9.44\text{ m}^2$ to square centimetres
b. $3.44\times 10^8\text{ mm}^3$ to cubic meters

Solution

a. $94\text{,}400\text{ cm}^2$
b. $0.344\text{ m}^3$

8. Perform the following conversions.

a. $0.00444\text{ cm}^3$ to cubic meters
b. $8.11\times 10^2\text{ m}^2$ to square nanometres

9. Why would it be inappropriate to convert square centimetres to cubic meters?

Solution

One is a unit of area, and the other is a unit of volume.

10. Why would it be inappropriate to convert from cubic meters to cubic seconds?

11. Perform the following conversions.

a. $45.0$ m/min to meters/second
b. $0.000444$ m/s to micrometers/second
c. $60.0$ km/h to kilometres/second

Solution

a. $0.75$ m/s
b. $444$ µm/s
c. $1.666\times10^{−2}$ km/s

12. Perform the following conversions.

a. $3.4\times10^2$ cm/s to centimetres/minute
b. $26.6$ mm/s to millimetres/hour
c. $13.7$ kg/L to kilograms/millilitres

13. Perform the following conversions.

a. $0.674$ kL to millilitres
b. $2.81\times10^{12}$ mm to kilometres
c. $94.5$ kg to milligrams

Solution

a. $674\text{,}000$ mL
b. $2.81\times10^6$ km
c. $9.45\times10^7$ mg

14. Perform the following conversions.

a. $6.79\times10^{−6}$ kg to micrograms
b. $1.22$ mL to kilolitres
c. $9.508\times10^{−9}$ ks to milliseconds

15. Perform the following conversions.

a. $6.77\times10^{14}$ ms to kiloseconds
b. $34\text{,}550\text{,}000$ cm to kilometres

Solution

a. $6.77\times10^8$ ks
b. $345.5$ km

16. Perform the following conversions.

a. $4.701\times10^{15}$ mL to kilolitres
b. $8.022\times10^{−11}$ ks to microseconds

17. Perform the following conversions. Note that you will have to convert units in both the numerator and the denominator.

a. $88$ ft/s to miles/hour (Hint: use $5\text{,}280\text{ ft}=1\text{ mi}.$)
b. $0.00667$ km/h to meters/second

Solution

a. $6.0\times10^1$ mi/h
b. $0.00185$ m/s

18. Perform the following conversions. Note that you will have to convert units in both the numerator and the denominator.

a. $3.88\times10^2$ mm/s to kilometres/hour
b. $1.004$ kg/L to grams/millilitre

19. What is the area in square millimetres of a rectangle whose sides are $2.44\text{ cm}\times6.077\text{ cm}$? Express the answer to the proper number of significant figures.

Solution

$1.48\times103\text{ mm}^2$

20. What is the volume in cubic centimetres of a cube with sides of $0.774$ m? Express the answer to the proper number of significant figures.

21. The formula for the area of a triangle is $\frac12\times\text{base}\times\text{height}$. What is the area of a triangle in square centimetres if its base is $1.007$ m and its height is $0.665$ m? Express the answer to the proper number of significant figures.

Solution

$3.35\times10^3\text{ cm}^2$

22. The formula for the area of a triangle is $\frac12\times\text{base}\times\text{height}$. What is the area of a triangle in square meters if its base is $166$ mm and its height is $930.0$ mm? Express the answer to the proper number of significant figures.