Lessons 32: Metric System

New Concept

The system of measurement used throughout most of the world is the metric system. It is a decimal system where units differ by powers of $10$, such as

What’s next

Next, you'll see worked examples for converting metric units and solve problems comparing them to U.S. Customary measurements.

Property

The metric system is a decimal system where units in a category differ by a power of $10$. Prefixes indicate the multiplier of the basic unit, such as a meter. $1000 \text{ mm} = 100 \text{ cm} = 1 \text{ m} = 0.001 \text{ km}$.

Examples

$5 \text{ kilometers is } 5 \times 1000 = 5000 \text{ meters}.$
$300 \text{ centimeters is } 300 \div 100 = 3 \text{ meters}.$
$2 \text{ meters is } 2 \times 100 = 200 \text{ centimeters}.$

Explanation

Think of it like our money system! Just as 100 cents make one dollar, 100 centimeters make one meter. Converting is as simple as moving a decimal point, which is way easier than remembering that 5,280 feet make a mile. It’s a system built on the magic of ten!

Property

The liter (L) is the basic unit of capacity in the metric system. $1000$ milliliters (mL) $= 1$ liter (L).

Examples

$\text{A 2-liter bottle can hold } 2 \times 1000 = 2000 \text{ mL of beverage}.$
$\text{A recipe that needs 500 mL of water requires } 500 \div 1000 = 0.5 \text{ L}.$

Explanation

Imagine your favorite soda bottle—that’s usually 2 liters! A liter holds a bit more liquid than a quart. For tiny amounts, like medicine or a cool science experiment, we use milliliters. It takes exactly 1000 of those little mL drops to fill up one whole liter bottle.

Property

The kilogram (kg) is the basic unit of mass in the metric system. $1000$ grams (g) $= 1$ kilogram (kg) and $1000$ milligrams (mg) $= 1$ gram (g).

Examples

$\text{To get 1 gram of vitamin C, you need four 250-mg tablets, since } 4 \times 250 = 1000 \text{ mg}.$
$\text{A cat with a mass of 3.5 kg has a mass of } 3.5 \times 1000 = 3500 \text{ g}.$

Explanation

A kilogram feels like a big textbook and weighs about 2.2 pounds. For lighter things, like a paperclip, we use grams. For super tiny things like vitamins, we use milligrams. It's a simple system where everything is based on powers of 1000, making conversions a breeze!