Using Properties to Convert Traditional and Metric Units

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.

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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

Why does multiplying by a conversion factor not change the measurement?

A conversion factor is a fraction equal to 1 (e.g., 100 \(\color{blue}{\frac{\text{ cm }}{1}}\) \(\color{blue}{m = 1}\)). Multiplying any value by 1 does not change its magnitude — only the unit label changes.

Which way do I put the conversion fraction?

Put the unit you want to remove in the denominator so it cancels with the same unit in the original measurement, and put the unit you want to keep in the numerator.

Do I need to memorize customary-to-metric conversions for the GED?

The GED Math test usually provides a formula sheet. Focus on understanding how to use a conversion factor; the specific numbers will be given or can be approximated (e.g., 1 in ≈ 2.54 cm).

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