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

Why is the metric system easier to use than U.S. customary units?

Every metric conversion is a power of 10, so you only need to move the decimal point. U.S. customary conversions use irregular numbers like 12 inches per foot, 3 feet per yard, and 5,280 feet per mile, which require more memorization.

What is the difference between mass and weight in the metric system?

In everyday language they are often used interchangeably, but technically mass (measured in grams or kilograms) is the amount of matter in an object, while weight is the gravitational force on that mass. In metric science, mass is measured in kilograms and weight in Newtons.

How do I remember the metric prefixes in order?

Use the mnemonic King Henry Died By Drinking Cold Milk: Kilo, Hecto, Deka, Base, Deci, Centi, Milli.

Related Topics

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