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.
