Measurement and Geometry Unit

3.1 Unit Conversions in the Metric System

Because of the historical connections between the United States and England, the United States adopted the English system rather than the metric system of England’s former enemy, France. Today, the United States is the only industrialized country that has not adopted the metric system as its official system of measurement. However, in the United States, the metric system is widely used in many areas, including science and photography, but not carpentry.

Part I: Discovering the Metric System

Examine a meter stick and complete the following.

  1. Find a centimeter on your meter stick.

  2. How many centimeters are in a meter?

    There are 100 centimeters in a meter.

  3. The millimeter is the smallest unit of measure on your meter stick. How many millimeters are in a centimeter?

    There are 10 millimeters in a centimeter.

  4. How many millimeters are in a meter?

    There are 1000 millimeters in a meter.

  5. What is your height in centimeters?

  6. What is your height in millimeters?

Part II: Conversions Within The Metric System

From the above exercise, you see how meters, centimeters, and millimeters are related by powers of 10. This same relationship holds for all metric measures, and it makes conversions within the metric system easier than those in the customary system.

The metric prefixes are presented in the following table.

Prefix kilo- hecto- deka- meters
liters
grams		 deci- centi- milli-
Symbol k h dk m
L
g		 d c m
Meaning 1000 100 10 1 \(\frac1{10}\) \(\frac1{100}\) \(\frac1{1000}\)

Metric Lengths

Every metric length measurement includes one of these prefixes in front of the basic length unit, the meter. For most everyday measures, kilometers (km), meters (m), centimeters (cm), and millimeters (mm) are sufficient.

Example: 350 cm = ________ m.

Solution: Since there are 100 cm in a meter, divide 350cm by 100 to convert to meters:

350 ÷ 100 = 3.50.

You can also use a prefix chart and see that to go from centimeters to meters, you move the decimal two places to the left.

Or, \(\frac{350\;cm}1\;\times\;\frac{1\;m}{100\;cm}=\frac{350\;m}{100}=3.5\;m\)

  1. 0.5 m = _______mm

    \(\frac{0.5\;m}{1}\;\times\frac{1000\;mm}{1\;m}=500\;mm\)

  2. 80 mm = _______cm

    \(\frac{80\;mm}{1}\;\times\frac{1\;cm}{10\;mm}=8\;cm\)

  3. 1 kilometer is _______ meters (about 3/5 of a mile).

    \(\frac{1\;km}{1}\;\times\frac{1000\;m}{1\;km}=1000\;m\)

  4. 16 cm = ______mm

    \(\frac{16\;cm}{1}\;\times\frac{10\;mm}{1\;cm}=160\;mm\)

  5. List the following measurements in increasing order: 37 m, 46 cm, 871 mm, 3 km, 137 cm.

    6. 37 m = 37 m

    46 cm = 0.46 m

    871 mm = 0.871 m

    3 km = 3000 m

    137 cm = 1.37 m

    46 cm, 871 mm, 137 cm, 37 m, 3 km

  6. Lynn wants to swim 1 km in a 50 m-long pool. How many pool lengths must she swim?

    7. \( \begin{equation} \frac{1}{50 m} \times \frac{1000 m}{1 k m}=20 \text { lengths } / k m \end{equation} \)



Metric Mass

The gram (g) is the basic unit of mass in the metric system.

  1. 80g = _______kg

    \(\frac{80\;g}{1}\;\times\frac{1\;kg}{1000\;g}=0.08\;kg\)

  2. 37mg = ______g

    \(\frac{37\;mg}{1}\;\times\frac{1\;g}{1000\;mg}=0.037\;g\)

  3. 65g = ______mg

    \(\frac{65\;g}{1}\;\times\frac{1000\;mg}{1\;g}=65,000\;mg\)

  4. 0.082kg = ______g

    \(\frac{0.082\;kg}{1}\;\times\frac{1000\;g}{1\;kg}=82\;g\)

  5. A box contains 4 kg of paper clips. Each paper clip has a mass of about 0.8 g. About how many paper clips are in the box?

    6. \(\frac{4\;kg}1\;\times\frac{1000\;g}{1\;kg}\times\;\frac{1\;paper\;clip}{0.8\;g}=5000\)

    5000 paper clips

  6. A metric ton is 1,000 kilograms. How many metric tons is a car that weighs 2,480 kg?

    7. \(\frac{2480\;kg}{1\;car}\;\times\frac{1\;metric\;ton}{1000\;kg}=2.48\)

    2.48 metric tons

Metric Capacity

The liter (L) is the metric unit for capacity.

  1. 346 mL = ______L

    \(\frac{346\;mL}{1}\;\times\frac{1\;L}{1000\;mL}=0.346\;L\)

  2. 2 L = _______mL

    \(\frac{2\;L}{1}\;\times\frac{1000\;mL}{1\;L}=2000\;mL\)

  3. A container holds 3.24 liters of milk. How many milliliters is that?

    4. \(\frac{3.24\;L}{1\;container}\;\times\frac{1000\;mL}{1\;L}=3240\)

    3240 ml

  4. A nurse wants to give a patient 0.3 mg IV. The drug comes in a solution containing 0.5 mg per 2 mL. How many milliliters should be used?

    5. \(\begin{equation} \frac{2\; m l}{0.5 \;m g} \times \frac{0.3\; m g}{1\; IV}=1.2\; m l / IV \end{equation} \)