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The metric system of measurement takes advantage of our base ten number system. The advantage of the metric system over the United States system is that in the metric system it is possible to convert from one unit of measure to another simply by multiplying or dividing the given number by a power of 10. This means we can make a conversion simply by moving the decimal point to the right or the left.
Common units of measure in the metric system are the meter (for length), the liter (for volume), and the gram (for mass). To each of the units can be attached a prefix. The metric prefixes along with their meaning are listed below.
For example, if length is being measured,
1 kilometer is equivalent to 1000 meters.
1 centimeter is equivalent to one hundredth of a meter.
1 millimeter is equivalent to one thousandth of a meter.
Let's note three characteristics of the metric system that occur in the metric table of measurements.
The following table provides a summary of the relationship between the basic unit of measure (meter, gram, liter) and each prefix, and how many places the decimal point is moved and in what direction.
kilo hecto deka unit deci centi milli
Basic Unit to Prefix | Move the Decimal Point | |
unit to deka | 1 to 10 | 1 place to the left |
unit to hector | 1 to 100 | 2 places to the left |
unit to kilo | 1 to 1,000 | 3 places to the left |
unit to deci | 1 to 0.1 | 1 place to the right |
unit to centi | 1 to 0.01 | 2 places to the right |
unit to milli | 1 to 0.001 | 3 places to the right |
Listed below, in the unit conversion table, are some of the common metric units of measure.
Unit Conversion Table | ||
Length | $1\text{kilometer}(\text{km})=\text{1,000 meters}(m)$ | $\mathrm{1,}\text{000}\times 1\text{m}$ |
$1\text{hectometer}(\text{hm})=\text{100 meters}$ | $\text{100}\times 1\text{m}$ | |
$1\text{dekameter}(\text{dam})=\text{10 meters}$ | $\text{10}\times 1\text{m}$ | |
1 meter (m) | $1\times 1\text{m}$ | |
$1\text{decimeter}(\text{dm})=\frac{1}{\text{10}}\text{meter}$ | $\text{.}1\times 1\text{m}$ | |
$1\text{centimeter}(\text{cm})=\frac{1}{\text{100}}\text{meter}$ | $\text{.}\text{01}\times 1\text{m}$ | |
$1\text{millimeter}(\text{mm})=\frac{1}{\text{1,000}}\text{meter}$ | $\text{.}\text{001}\times 1\text{m}$ | |
Mass | $\text{1 kilogram}(\text{kg})=\text{1,000 grams}(g)$ | $\mathrm{1,}\text{000}\times 1\text{g}$ |
$\text{1 hectogram}(\text{hg})=\text{100 grams}$ | $\text{100}\times 1\text{g}$ | |
$\text{1 dekagram}(\text{dag})=\text{10 grams}$ | $\text{10}\times 1\text{g}$ | |
1 gram (g) | $1\times 1\text{g}$ | |
$\text{1 decigram}(\text{dg})=\frac{1}{\text{10}}\text{gram}$ | $\text{.}1\times 1\text{g}$ | |
$\text{1 centigram}(\text{cg})=\frac{1}{\text{100}}\text{gram}$ | $\text{.}\text{01}\times 1\text{g}$ | |
$\text{1 milligram}(\text{mg})=\frac{1}{\text{1,000}}\text{gram}$ | $\text{.}\text{001}\times 1\text{g}$ | |
Volume | $\text{1 kiloliter}(\text{kL})=\mathrm{1,}\text{000}\text{liters}(L)$ | $\mathrm{1,}\text{000}\times 1\text{L}$ |
$\text{1 hectoliter}(\text{hL})=\text{100}\text{liters}$ | $\text{100}\times 1\text{L}$ | |
$\text{1 dekaliter}(\text{daL})=\text{10}\text{liters}$ | $\text{10}\times 1\text{L}$ | |
1 liter (L) | $1\times 1\text{L}$ | |
$\text{1 deciliter}(\text{dL})=\frac{1}{\text{10}}\text{liter}$ | $\text{.}1\times 1\text{L}$ | |
$\text{1 centiliter}(\text{cL})=\frac{1}{\text{100}}\text{liter}$ | $\text{.}\text{01}\times 1\text{L}$ | |
$\text{1 milliliter}(\text{mL})=\frac{1}{\mathrm{1,}\text{000}}\text{liter}$ | $\text{.}\text{001}\times 1\text{L}$ | |
Time | Same as the United States system |
We can also convert from one metric unit to another using unit fractions. Both methods are shown in [link] of [link] .
Convert 3 kilograms to grams.
Thus, $\text{3kg}=\text{3,000 g}$ .
Since we are converting to grams, and $\mathrm{1,}\text{000}g=\text{1 kg}$ , we choose the unit fraction $\frac{\text{1,000 g}}{\text{1 kg}}$ since grams is in the numerator.
$\begin{array}{ccc}\hfill \text{3 kg}& =& \text{3 kg}\cdot \frac{\text{1,000 g}}{\text{1 kg}}\hfill \\ & =& 3\overline{)\text{kg}}\cdot \frac{\text{1,000 g}}{1\overline{)\text{kg}}}\hfill \\ & =& 3\cdot \mathrm{1,000}\text{g}\hfill \\ & =& \text{3,000 g}\hfill \end{array}$
Convert 67.2 hectoliters to milliliters.
Thus, $\text{67}\text{.}\text{2 hL}=\text{6,720,000 mL}$ .
Convert 100.07 centimeters to meters.
Thus, $\text{100}\text{.}\text{07 cm}=\text{1}\text{.}\text{0007 m}$ .
Convert 0.16 milligrams to grams.
Thus, $0\text{.}\text{16}\text{mg}=\text{0}\text{.}\text{00016 g}\text{.}$
Convert 411 kilograms to grams.
411,000 g
Convert 5.626 liters to centiliters.
562.6 cL
Convert 80 milliliters to kiloliters.
0.00008 kL
Convert 150 milligrams to centigrams.
15 cg
Convert 2.5 centimeters to meters.
0.025 m
Make each conversion.
87 m to cm
8,700 cm
905 L to mL
16,005 mg to g
16.005 g
48.66 L to dL
11.161 kL to L
11,161 L
521.85 cm to mm
1.26 dag to dg
126 dg
99.04 dam to cm
0.51 kL to daL
5.1 daL
0.17 kL to daL
0.05 m to dm
0.5 dm
0.001 km to mm
8.106 hg to cg
81,060 cg
17.0186 kL to mL
3 cm to m
0.03 m
9 mm to m
4 g to mg
4,000 mg
2 L to kL
6 kg to mg
6,000,000 mg
7 daL to mL
( [link] ) Find the value of $\frac{5}{8}-\frac{1}{3}+\frac{3}{4}$ .
$\frac{\text{25}}{\text{24}}=1\frac{1}{\text{24}}$
( [link] ) Solve the proportion: $\frac{9}{x}=\frac{\text{27}}{\text{60}}$ .
( [link] ) Use the method of rounding to estimate the sum: $\mathrm{8,}\text{226}+\mathrm{4,}\text{118}$ .
12,300 (12,344)
( [link] ) Use the clustering method to estimate the sum: $\text{87}+\text{121}+\text{118}+\text{91}+\text{92}$ .
( [link] ) Convert 3 in. to yd.
$0\text{.}\text{08}\overline{3}$ yard
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