Metric Units

The metric system is the international standard for measurement, and understanding metric units is essential in Algebra 1, science, and everyday life around the world. Every metric conversion is a power of ten, which makes the math clean and predictable: you simply move the decimal point left or right based on the prefix. This guide explains the most important metric units, their prefixes, and how to convert between them, with worked examples, two video lessons, and practice problems.

What Are Metric Units?

The metric system organizes measurements around three base units:

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• Length: meter (m)
• Mass: gram (g)
• Volume: liter (L)

Each base unit is scaled using prefixes that represent powers of ten.

Metric Prefixes

The most common metric prefixes, from largest to smallest:

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

Memory tip: King Henry Died By Drinking Cold Milk (kilo, hecto, deka, base, deci, centi, milli).

How to Convert Metric Units

Moving the decimal

Each step up the prefix ladder divides by 10 (moves the decimal left); each step down multiplies by 10 (moves the decimal right).

Example: \(\color{blue}{4.5 \text{ km }}\) to \(\color{blue}{m}\), kilo is 3 steps above base, so multiply by 10³ = 1,000:
\(\color{blue}{4.5 \times 1,000 = 4,500 m}\)

Using conversion factors

Write the conversion as a fraction equal to 1 and cancel units:

Example: \(\color{blue}{350 \text{ mm } \times (1 \frac{\text{ cm }}{10} \text{ mm }) = 35 \text{ cm }}\)

Step-by-Step Summary

1. Identify the starting unit and the target unit.
2. Determine how many powers of 10 apart they are on the prefix scale.
3. If converting to a smaller unit (e.g., km to m), multiply.
4. If converting to a larger unit (e.g., g to kg), divide.
5. Move the decimal point the correct number of places.

Watch: Introduction to the Metric System (Video Lesson)

Math Antics introduces the metric system, its prefixes, and how to move between units using powers of ten:

Metric Units – Worked Examples

Example 1: Convert 4.5 km to meters.

1 \(\color{blue}{\text{ km } = 1}\),000 m:
\(\color{blue}{4.5 \times 1,000 = 4,500 m}\)

Example 2: Convert 350 mm to centimeters.

1 \(\color{blue}{\text{ cm } = 10}\) mm:
\(\color{blue}{350 \div 10 = 35 \text{ cm }}\)

Example 3: Convert 2,500 g to kilograms.

1 \(\color{blue}{\text{ kg } = 1}\),000 g:
\(\color{blue}{2,500 \div 1,000 = 2.5 \text{ kg }}\)

Example 4: Convert 0.75 L to milliliters.

1 \(\color{blue}{L = 1}\),000 mL:
\(\color{blue}{0.75 \times 1,000 = 750 \text{ mL }}\)

Example 5: Convert 6.2 km to centimeters.

1 \(\color{blue}{\text{ km } = 1}\),000 m and 1 \(\color{blue}{m = 100}\) cm, so 1 \(\color{blue}{\text{ km } = 100}\),000 cm:
\(\color{blue}{6.2 \times 100,000 = 620,000 \text{ cm }}\)

More Practice: Converting Between Metric Units (Video)

Khan Academy walks through multiple metric unit conversions using conversion factors and the prefix ladder:

Exercises for Metric Units

1. Convert 3.2 km to meters.
2. Convert 800 cm to meters.
3. Convert 4,750 g to kilograms.
4. Convert 2.3 L to milliliters.
5. Convert 55 mm to centimeters.
6. Convert 0.006 km to centimeters.

Answers

1. \(\color{blue}{3,200 m}\)
2. \(\color{blue}{8 m}\)
3. \(\color{blue}{4.75 \text{ kg }}\)
4. \(\color{blue}{2,300 \text{ mL }}\)
5. \(\color{blue}{5.5 \text{ cm }}\)
6. \(\color{blue}{600 \text{ cm }}\)

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Want More Practice?

We haven’t published a worksheet built specifically for Metric Units just yet. In the meantime, the free worksheets below cover closely related skills and concepts. If you’d like extra practice, download any that look helpful, complete the problems, and check your work. They’re a great way to reinforce what you learned on this page and strengthen the foundations this topic builds on:

• Download Direct Variation Worksheet
• Download Personal Financial Literacy Worksheet

Frequently Asked Questions

What are metric units of measurement?

Metric units are the measurement units of the metric system, which is used in science and in most countries. The main base units are the meter for length, the gram (or kilogram) for mass, and the liter for volume. Prefixes such as kilo-, centi- and milli- show multiples of 10, so 1 kilometer is 1,000 meters.

What is the difference between metric units and imperial units?

Metric units are based on powers of 10, so converting only means moving the decimal point. Imperial units, such as inches, feet, pounds and gallons, use uneven relationships like 12 inches in a foot and 5,280 feet in a mile. The United States mainly uses customary units in daily life, while science uses metric.

How do you convert metric units?

Find how many places apart the two prefixes are, then move the decimal point that many places. Going to a smaller unit, move it right (multiply); going to a larger unit, move it left (divide). For example, 3.5 kilometers = 3,500 meters, and 250 centimeters = 2.5 meters.

What are the metric units of length from smallest to largest?

The common metric units of length from smallest to largest are millimeter, centimeter, decimeter, meter, dekameter, hectometer and kilometer. Each unit is 10 times the one before it, so 10 mm = 1 cm, 100 cm = 1 m, and 1,000 m = 1 km. In everyday problems you will mostly see mm, cm, m and km.

What is the metric unit of mass?

The basic metric unit of mass is the gram, and the official SI base unit is the kilogram, which equals 1,000 grams. Very small amounts are measured in milligrams (1,000 mg = 1 g). A paper clip has a mass of about 1 gram, while a liter of water has a mass of about 1 kilogram.

What is the metric unit for volume?

The liter is the everyday metric unit for liquid volume, and milliliters are used for small amounts (1 L = 1,000 mL). One milliliter equals one cubic centimeter, so a 2 cm × 3 cm × 5 cm box holds 30 cm³, or 30 mL. In science, the cubic meter is the SI unit of volume.

Related Topics

• Convert Units of Measurement
• Unit Rates and Rates
• Arithmetic Sequences
• Writing Linear Equations