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

**Exercises: Significant Figures**

**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. [latex]1\text{,}000\text{ mL}/1\text{ L}[/latex] and [latex]1\text{ L}/1\text{,}000\text{ mL}[/latex]

b. [latex]1\text{,}000\text{,}000\text{ μs}/1\text{ s}[/latex] and [latex]1\text{ s}/1\text{,}000\text{,}000\text{ μs}[/latex]

c. [latex]1\text{,}000\text{ m}/1\text{ km}[/latex] and [latex]1\text{ km}/1\text{,}000\text{ m}[/latex]

**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. [latex]5.4[/latex] km to meters**

**b. [latex]0.665[/latex] m to millimetres**

**c. [latex]0.665[/latex] m to kilometres**

**Solution**

a. [latex]5\text{,}400[/latex] m

b. [latex]665[/latex] mm

c. [latex]6.65\times10^{−4}[/latex] km

**4. Perform the following conversions.**

**a. [latex]90.6[/latex] mL to litres**

**b. [latex]0.00066[/latex] mL to litres**

**c. [latex]750[/latex] L to kilolitres**

**5. Perform the following conversions.**

**a. [latex]17.8[/latex] μg to grams**

**b. [latex]7.22\times10^2[/latex] kg to grams**

**c. [latex]0.00118[/latex] g to nanograms**

**Solution**

a. [latex]1.78\times10^{−5}[/latex] g

b. [latex]7.22\times10^5[/latex] g

c. [latex]1.18\times10^6[/latex] ng

**6. Perform the following conversions.**

**a. [latex]833[/latex] ns to seconds**

**b. [latex]5.809[/latex] s to milliseconds**

**c. [latex]2.77\times10^6[/latex] s to megaseconds**

**7. Perform the following conversions.**

**a. [latex]9.44\text{ m}^2[/latex] to square centimetres
**

**b. [latex]3.44\times 10^8\text{ mm}^3[/latex] to cubic meters**

**Solution**

a. [latex]94\text{,}400\text{ cm}^2[/latex]^{
}b. [latex]0.344\text{ m}^3[/latex]

**8. Perform the following conversions.**

**a. [latex]0.00444\text{ cm}^3[/latex] to cubic meters
b. [latex]8.11\times 10^2\text{ m}^2[/latex] 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. [latex]45.0[/latex] m/min to meters/second**

**b. [latex]0.000444[/latex] m/s to micrometers/second**

**c. [latex]60.0[/latex] km/h to kilometres/second**

**Solution**

a. [latex]0.75[/latex] m/s

b. [latex]444[/latex] µm/s

c. [latex]1.666\times10^{−2}[/latex] km/s

**12. Perform the following conversions.**

**a. [latex]3.4\times10^2[/latex] cm/s to centimetres/minute**

**b. [latex]26.6[/latex] mm/s to millimetres/hour**

**c. [latex]13.7[/latex] kg/L to kilograms/millilitres**

**13. Perform the following conversions.**

**a. [latex]0.674[/latex] kL to millilitres**

**b. [latex]2.81\times10^{12}[/latex] mm to kilometres**

**c. [latex]94.5[/latex] kg to milligrams**

**Solution**

a. [latex]674\text{,}000[/latex] mL

b. [latex]2.81\times10^6[/latex] km

c. [latex]9.45\times10^7[/latex] mg

**14. Perform the following conversions.**

**a. [latex]6.79\times10^{−6}[/latex] kg to micrograms**

**b. [latex]1.22[/latex] mL to kilolitres**

**c. [latex]9.508\times10^{−9}[/latex] ks to milliseconds**

**15. Perform the following conversions.**

**a. [latex]6.77\times10^{14}[/latex] ms to kiloseconds**

**b. [latex]34\text{,}550\text{,}000[/latex] cm to kilometres**

**Solution**

a. [latex]6.77\times10^8[/latex] ks

b. [latex]345.5[/latex] km

**16. Perform the following conversions.**

**a. [latex]4.701\times10^{15}[/latex] mL to kilolitres**

**b. [latex]8.022\times10^{−11}[/latex] ks to microseconds**

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

**a. [latex]88[/latex] ft/s to miles/hour (Hint: use [latex]5\text{,}280\text{ ft}=1\text{ mi}.[/latex])**

**b. [latex]0.00667[/latex] km/h to meters/second**

**Solution**

a. [latex]6.0\times10^1[/latex] mi/h

b. [latex]0.00185[/latex] m/s

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

a. [latex]3.88\times10^2[/latex] mm/s to kilometres/hour

b. [latex]1.004[/latex] kg/L to grams/millilitre

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

**Solution**

[latex]1.48\times103\text{ mm}^2[/latex]

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

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

**Solution**

[latex]3.35\times10^3\text{ cm}^2[/latex]

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