Introduction to Conversions
With all the different systems of units in use throughout the world, the business of conversion from one system to another has become the subject matter for Web sites. Nevertheless, in order to get familiar with how units relate to each other, it’s a good idea to do a few manual calculations before going online and letting your computer take over the “dirty work.” The problems below are some examples; you can certainly think of other unit-conversion situations that you are likely to encounter in your everyday affairs. Table 4-1 can serve as a guide for converting base units.
Dimensions
When converting from one unit system to another, always be sure you’re talking about the same quantity or phenomenon. For example, you cannot convert meters squared to centimeters cubed, or candela to meters per second. You must keep in mind what you’re trying to express, and be sure you are not, in effect, trying to change an apple into a drinking glass.
The particular thing that a unit quantifies is called the dimension of the quantity or phenomenon. Thus, meters per second, feet per hour, and furlongs per fortnight represent expressions of the speed dimension; seconds, minutes, hours, and days are expressions of the time dimension.
Conversion Between Different Systems of Units Practice Problems
Practice 1
Suppose you step on a scale and it tells you that you weigh 120 pounds. How many kilograms does that represent?
Solution 1
Assume you are on the planet earth, so your mass-to-weight conversion can be defined in a meaningful way. (Remember, mass is not the same thing as weight.) Use Table 4-1. Multiply by 0.4535 to get 54.42 kg. Because you are given your weight to only three significant figures, you should round this off to 54.4 kg.
Practice 2
You are driving in Europe and you see that the posted speed limit is 90 kilometers per hour (km/hr). How many miles per hour (mi/hr) is this?
Solution 2
In this case, you only need to worry about miles versus kilometers; the “per hour” part doesn’t change. So you convert kilometers to miles. First remember that 1km = 1000m; then 90km = 90,000m = 9.0 × 10 ^{4} m. The conversion of meters to statute miles (these are the miles used on land) requires that you multiply by 6.214 × 10 ^{–4} . Therefore, you multiply 9.0 × 10 ^{4} by 6.214 × 10 ^{–4} to get 55.926. This must be rounded off to 56, or two significant figures, because the posted speed limit quantity, 90, only goes that far.
Practice 3
How many feet per second is the above-mentioned speed limit? Use the information in Table 4-1.
Table 4-1 Conversions for base units in the International System (SI) to units in other systems. When no coefficient is given, it is exactly equal to 1.
To convert: |
To: |
Multiply by: |
Conversely, multiply by: |
meters (m) |
nanometers (nm) |
10 ^{9} |
10 ^{−9} |
meters (m) |
microns (m) |
10 ^{6} |
10 ^{−6} |
meters (m) |
millimeters (mm) |
10 ^{3} |
10 ^{−3} |
meters (m) |
centimeters (cm) |
10 ^{2} |
10 ^{−2} |
meters (m) |
inches (in) |
39.37 |
0.02540 |
meters (m) |
feet (ft) |
3.281 |
0.3048 |
meters (m) |
yards (yd) |
1.094 |
0.9144 |
meters (m) |
kilometers (km) |
10 ^{−3} |
10 ^{3} |
meters (m) |
statute miles (mi) |
6.214×10 ^{−4} |
1.609×10 ^{3} |
meters (m) |
nautical miles |
5.397×10 ^{−4} |
1.853×10 ^{3} |
kilograms (kg) |
nanograms (ng) |
10 ^{12} |
10 ^{−12} |
kilograms (kg) |
micrograms (mg) |
10 ^{9} |
10 ^{−9} |
kilograms (kg) |
milligrams (mg) |
10 ^{6} |
10 ^{−6} |
kilograms (kg) |
grams (g) |
10 ^{3} |
10 ^{−3} |
kilograms (kg) |
ounces (oz) |
35.28 |
0.02834 |
kilograms (kg) |
pounds (lb) |
2.205 |
0.4535 |
kilograms (kg) |
English tons |
1.10 ^{3} −10 ^{−3} |
907.0 |
seconds (s) |
minutes (min) |
0.01667 |
60.00 |
seconds (s) |
hours (h) |
2.778×10 ^{−4} |
3.600×10 ^{3} |
seconds (s) |
days (dy) |
1.157×10 ^{−5} |
8.640×10 ^{4} |
seconds (s) |
years (yr) |
3.169×10 ^{−8} |
3.156×10 ^{7} |
degrees Kelvin (°K) |
degrees Celsius (°C) |
Subtract 273 |
Add 273 |
degrees Kelvin (°K) |
degrees Fahrenheit (°F) |
Multiply by 1.80, then subtract 459 |
Multiply by 0.556, then add 255 |
degrees Kelvin (°K) |
degrees Rankine (°R) |
1.80 |
0.556 |
amperes (A) |
carriers per second |
6.24×10 ^{18} |
1.60×10 ^{−19} |
amperes (A) |
nanoamperes (nA) |
10 ^{9} |
10 ^{−9} |
amperes (A) |
microamperes (mA) |
10 ^{6} |
10 ^{−6} |
amperes (A) |
milliamperes (mA) |
10 ^{3} |
10 ^{−3} |
candela (cd) |
microwatts per steradian (mW/sr) |
1.464×10 ^{3} |
6.831×10 ^{−4} |
candela (cd) |
milliwatts per steradian (mW/sr) |
1.464 |
0.6831 |
candela (cd) |
watts per steradian (W/sr) |
1.464×10 ^{−3} |
683.1 |
moles (mol) |
coulombs (C) |
9.65×10 ^{4} |
1.04×10 ^{−5} |
Solution 3
Let’s convert kilometers per hour to kilometers per second first. This requires division by 3600, the number of seconds in an hour. Thus, 90km/hr = 90/3600 km/s = 0.025 km/s. Next, convert kilometers to meters. Multiply by 1000 to obtain 25m/s as the posted speed limit. Finally, convert meters to feet. Multiply 25 by 3.281 to get 82.025. This must be rounded off to 82 ft/sec because the posted speed limit is expressed to only two significant figures.
Find practice problems and solutions for these concepts at: Unites of Measurement Practice Test.
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