Using Properties to Convert Traditional and Metric Units

How to using properties to convert traditional and metric units, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

The United States commonly uses two systems of measurement: the traditional (customary) system (inches, pounds, gallons) and the metric system (meters, kilograms, liters). On the GED test you may need to convert both within each system and between the two systems. Using the multiplicative property of conversion factors — multiplying by a fraction equal to 1 — makes every conversion systematic and reliable.

What Is a Conversion Factor?

A conversion factor is a fraction equal to 1 because the numerator and denominator represent the same quantity in different units. For example, \(\color{blue}{12 \frac{\text{ in }}{1} \text{ ft } = 1}\). Multiplying any measurement by a conversion factor changes the units without changing the value.

Rule: Set up the fraction so the unit you want to eliminate cancels (is in the opposite position), and the unit you want to keep remains.

Metric Prefix Chart

• kilo- \(\color{blue}{(k) = 1}\),000  •  hecto- \(\color{blue}{(h) = 100}\)  •  deka- \(\color{blue}{(\text{ da }) = 10}\)
• base unit \(\color{blue}{(m, g, L) = 1}\)
• deci- \(\color{blue}{(d) = 0.1}\)  •  centi- \(\color{blue}{(c) = 0.01}\)  •  milli- \(\color{blue}{(m) = 0.001}\)

To convert within metric: move the decimal left (to a larger unit) or right (to a smaller unit) by the number of steps between prefixes.

Common Metric Conversions

• 1 \(\color{blue}{\text{ km } = 1}\),000 m  •  1 \(\color{blue}{m = 100}\) \(\color{blue}{\text{ cm } = 1}\),000 mm
• 1 \(\color{blue}{\text{ kg } = 1}\),000 g  •  1 \(\color{blue}{g = 1}\),000 mg
• 1 \(\color{blue}{L = 1}\),000 mL

Common Customary-to-Metric Conversions

• 1 inch ≈ 2.54 cm  •  1 mile ≈ 1.609 km
• 1 pound ≈ 0.454 kg  •  1 kilogram ≈ 2.205 lb
• 1 gallon ≈ 3.785 L

Step-by-Step Summary

1. Write the original measurement.
2. Choose the conversion factor that cancels the unwanted unit.
3. Multiply: the unwanted unit cancels, leaving the desired unit.
4. Do the arithmetic (multiply or divide the numbers).
5. Round if needed and label the answer.

Watch: Unit Conversion Within the Metric System (Video Lesson)

Khan Academy explains metric prefixes and the conversion factor method clearly:

Worked Examples

Example 1: Convert 3.5 km to meters.

3.5 \(\color{blue}{\text{ km } \times (1,000 \frac{m}{1} \text{ km })}\) = 3,500 m

Example 2: Convert 250 cm to meters.

250 \(\color{blue}{\text{ cm } \times (1 \frac{m}{100} \text{ cm }) = \frac{250}{100}}\) = 2.5 m

Example 3: Convert 4,500 mL to liters.

4,500 \(\color{blue}{\text{ mL } \times (1 \frac{L}{1},000 \text{ mL }) = 4}\),\(\color{blue}{\frac{500}{1}}\),000 = 4.5 L

Example 4: A person weighs 2.8 kg. Convert to grams.

2.8 \(\color{blue}{\text{ kg } \times (1,000 \frac{g}{1} \text{ kg })}\) = 2,800 g

More Practice: Customary Conversions (Video)

This video demonstrates the same multiplicative approach applied to customary units with mixed numbers:

Exercises

1. Convert 5.2 km to meters.
2. Convert 850 mm to centimeters.
3. Convert 3,200 g to kilograms.
4. Convert 0.75 L to milliliters.
5. A runner completes 10 km. About how many miles is that? (Use 1 mi ≈ 1.609 km.)
6. Convert 180 cm to meters.

Answers

1. \(\color{blue}{5.2 \times 1}\),000 = 5,200 m
2. \(\color{blue}{850 \div 10}\) = 85 cm
3. 3,\(\color{blue}{200 \div 1}\),000 = 3.2 kg
4. \(\color{blue}{0.75 \times 1}\),000 = 750 mL
5. \(\color{blue}{10 \div 1.609}\) ≈ 6.21 mi
6. \(\color{blue}{180 \div 100}\) = 1.8 m

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Frequently Asked Questions

How do you convert between customary and metric systems?

Multiply by a conversion factor written as a fraction equal to 1, with the unit you want to cancel on the bottom. To change 10 inches to centimeters, use 2.54 cm / 1 in: 10 × 2.54 = 25.4 cm. To change 5 kilograms to pounds, use about 2.2 lb / 1 kg: 5 × 2.2 ≈ 11 lb. Watching the units cancel tells you the setup is right.

How do you do metric conversions?

Metric units go up and down by powers of 10, so you just move the decimal point. Going to a smaller unit, move it right; going to a larger unit, move it left. For example, 3.6 km = 3,600 m (three places right), and 450 mL = 0.45 L (three places left). The prefix order kilo, hecto, deka, base, deci, centi, milli shows how many places to move.

Is the metric system better than the customary system?

The metric system is easier to calculate with because every unit is 10, 100 or 1,000 times another, and it is used by most of the world and in science. The customary system is still common in the United States for everyday things like road distances, recipes and body weight. Since both appear on tests and in daily life, it helps to be comfortable converting between them.

How do you use a metric conversion chart?

Find the unit you have and the unit you want on the chart, then count the steps between them. Each step on a metric prefix chart is a factor of 10. From grams to milligrams is three steps toward the smaller unit, so 2.5 g = 2,500 mg. For customary-to-metric charts, read the factor in the row, such as 1 mile ≈ 1.61 km, and multiply.

What are metric and customary measurements?

They are two systems for measuring length, weight and capacity. Customary units include inches, feet, miles, ounces, pounds, cups and gallons. Metric units include millimeters, meters, kilometers, grams, kilograms, milliliters and liters. A few useful links between them: 1 inch = 2.54 cm exactly, 1 kg ≈ 2.2 lb, and 1 liter is a little more than 1 quart.

Related Topics

• Converting, Comparing, Adding and Subtracting Mixed Customary Units
• Customary Unit Conversions Involving Mixed Numbers and Fractions
• Compare the Temperatures Above and Below Zero
• Word Problems Involving Rates and Ratios
• Multiplying Mixed Numbers