The metric system is a system of measurement in which units are related by powers of 10. Its base units are the meter for length, the gram for mass and the liter for capacity. Prefixes name larger and smaller units: kilo- means 1,000, centi- means one hundredth and milli- means one thousandth, so 1 km = 1,000 m.
In Spanish
sistema métrico
Also called
metric units, International System of Units, SI units, decimal system of measurement
Count the steps between two prefixes and move the decimal point that many places: right for smaller units, left for larger units.
Formal definition and notation
The metric system is the decimal system of units that grew into the International System of Units (SI). Each quantity has one base unit, and every other unit of that quantity is the base unit times a power of 10 named by a prefix: kilo (103), hecto (102), deka (101), deci (10−1), centi (10−2) and milli (10−3). The SI base units are the meter, kilogram, second, ampere, kelvin, mole and candela; school math mostly uses the meter, gram (from the kilogram) and liter.
units of capacity (liquid volume); a capital L avoids confusion with the digit 1
Key facts
Every metric conversion is multiplying or dividing by 10, 100, 1,000 and so on, which just moves the decimal point.
Converting to a smaller unit gives a biggernumber (2 m = 200 cm); converting to a larger unit gives a smaller number.
The same prefixes work for every quantity: a kilometer is 1,000 meters, a kilogram is 1,000 grams and a kiloliter is 1,000 liters.
1 milliliter of water fills a cube 1 cm on each side: 1 mL = 1 cm3.
The United States mostly uses customary units (inches, pounds, gallons), but science, medicine and most of the world use the metric system.
Metric conversion rule
Metric conversion rule
new number = old number × 10k
k
the number of prefix steps you move toward smaller units (move right on the ladder); use a negative k when you move toward larger units
old number
the measurement you start with
From kilometers to meters is 3 steps right, so multiply by 103 = 1000: 4.2 km = 4,200 m. From milligrams to grams is 3 steps left, so divide by 1,000: 750 mg = 0.75 g.
Try it: convert metric units
Interactive
Type an amount and pick two mass units. Each step on the stairs moves the decimal point one place. Try kilograms to milligrams: 6 steps, so multiply by 1,000,000.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Metric System examples, step by step
Example 1: Kilograms to grams
Warm-up
A bag of flour has a mass of 2.5 kg. How many grams is that?
Kilo means 1,000, so 1 kg = 1,000 g.
Grams are a smaller unit, so the number gets bigger: multiply.
2.5 × 1000 = 2500.
Answer: The flour has a mass of 2,500 g.
Example 2: Millimeters to meters
Core
A pencil is 175 mm long. Write its length in meters and in centimeters.
Meters are 3 prefix steps larger than millimeters (milli to centi to deci to meter), so divide by 1,000.
175 ÷ 1000 = 0.175 m.
Centimeters are 1 step larger than millimeters, so divide by 10: 175 ÷ 10 = 17.5 cm.
Answer: The pencil is 0.175 m, or 17.5 cm, long.
Example 3: Compare mixed units
Test-style
A nurse gives three doses of 250 mL each from a 1.5 L bag of saline. How many milliliters are left in the bag?
Write both amounts in the same unit: 1.5 L = 1.5 × 1000 = 1500 mL.
Total given: 3 × 250 = 750 mL.
Left: 1500 − 750 = 750 mL.
Answer: 750 mL of saline are left in the bag.
Common mistakes
✗ MistakeConverting 3 m to centimeters by dividing: 3 ÷ 100 = 0.03 cm.
✓ InsteadCentimeters are smaller, so multiply: 3 × 100 = 300 cm.
A smaller unit needs more of them to cover the same length, so the number must get bigger.
✗ MistakeTreating every step as 100 because “centi” is in many problems: 4 km = 400 m.
✓ Instead4 km = 4,000 m, because kilo means 1,000.
Each prefix step is a factor of 10. Kilo to base is 3 steps, so the factor is 1,000.
✗ MistakeAdding 2 m + 35 cm = 37.
✓ InsteadChange to one unit first: 2 m = 200 cm, so 200 cm + 35 cm = 235 cm (or 2.35 m).
You can only add measurements that use the same unit.
Not to be confused with
Metric Systemvs.Customary system
The US customary system uses inches, feet, pounds and gallons, with uneven steps such as 12 inches = 1 foot. Metric steps are always powers of 10.
Unit conversion is the process of changing units, in any system; the metric system is one set of units where that process is just moving the decimal point.
Quick check: 3 questions
Question 1 of 3
How many centimeters are in 4.6 meters?
Show answer and explanation
Answer: C. Centi means one hundredth, so 1 m = 100 cm and 4.6 × 100 = 460. 0.046 divides instead of multiplying, 46 uses 10, and 4,600 uses 1,000 (that would be millimeters).
Question 2 of 3
Which measurement equals 3,200 grams?
Show answer and explanation
Answer: A. Grams to kilograms is 3 steps to a larger unit, so divide by 1,000: 3200 ÷ 1000 = 3.2 kg. 32 and 320 divide by too little; 0.32 divides by 10,000.
Question 3 of 3
A bottle holds 750 mL. How many liters is that?
Show answer and explanation
Answer: C. Milli means one thousandth, so divide by 1,000: 750 ÷ 1000 = 0.75 L. 7.5 and 75 divide by 100 and 10; 0.075 divides by 10,000.
Metric System: frequently asked questions
What are the three main units of the metric system?
In school math the three base units are the meter for length, the gram for mass and the liter for capacity. Every other unit is one of these with a prefix, such as kilometer, milligram or milliliter. In science, the official SI base unit of mass is the kilogram, and there are seven SI base units in all, including the second for time.
How do you remember the metric prefixes in order?
From largest to smallest the common prefixes are kilo, hecto, deka, base unit, deci, centi, milli. Many students use a sentence whose words start with the same letters, such as “King Henry Died By Drinking Chocolate Milk.” Each step on that list is a factor of 10, so count the steps to know how far to move the decimal point.
Why is the metric system easier than the customary system?
Every metric unit is 10, 100 or 1,000 times another, so conversions are multiplication or division by a power of 10 and need no memorized factors. In the customary system the factors change: 12 inches in a foot, 3 feet in a yard, 5,280 feet in a mile and 16 ounces in a pound.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 4.MD.A.1, CCSS 5.MD.A.1
Cite this entry
Effortless Math Team. “Metric System.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/metric-system/
Flashcard
TermMetric Systemunits built on powers of 10
DefinitionMeasurement units linked by powers of 10: meter, gram, liter, with prefixes kilo (1,000), centi (0.01), milli (0.001). Example: 3 km = 3,000 m.
PowerA power is a number written as a base with an exponent, such as 53, or the value that results, 53 = 5 × 5 × 5 = 125. We say 125 is the third power of 5, or “5 to the third power”. The second power is called the square and the third power the cube.Number System · Grade 5, Grade 6, Grade 7MeterA meter (m) is a metric unit of length equal to 100 centimeters. It is the base unit of length in the metric system, a little over three feet (about 3.28 feet). A doorway is about 2 meters tall, and 1,000 meters make a kilometer. To change meters to centimeters, multiply by 100.Measurement · Grade 3, Grade 4, Grade 5KilogramA kilogram is the base unit of mass in the metric system (SI), equal to 1,000 grams. Its symbol is kg. A liter of water has a mass of about 1 kilogram, and 1 kilogram is about 2.2 pounds. Kilograms measure heavier things, such as people, bags of flour or luggage.Measurement · Grade 3, Grade 4, Grade 5GramA gram is a metric unit of mass, about the mass of a paper clip. Its symbol is g. There are 1,000 grams in a kilogram and 1,000 milligrams in a gram. Grams measure light things, such as food portions, coins and letters; heavier things are measured in kilograms.Measurement · Grade 3, Grade 4, Grade 5LengthLength is how long something is: the distance from one end of an object to the other. You measure it by counting equal units laid end to end with no gaps or overlaps, such as inches, feet, centimeters or meters. A new pencil is about 7 inches long.Measurement · Grade 1, Grade 2, Grade 3VolumeVolume measures the amount of space inside a three-dimensional figure, in cubic units such as cubic centimeters or cubic feet. You can find it by counting the unit cubes that fill the solid. For a rectangular prism, V = l × w × h; for any prism, it equals the area of the base multiplied by the height.Geometry · Grade 5, Grade 6, Grade 7Decimal PointA decimal point is the dot that separates the whole-number part of a number from its fractional part. Digits to its left are ones, tens and hundreds; digits to its right are tenths, hundredths and thousandths. In 46.25 the point sits between 6 ones and 2 tenths, and you read it aloud as “and”.Number System · Grade 4, Grade 5, Grade 6NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2KilometerA kilometer (km) is a metric unit of length equal to 1,000 meters, roughly six tenths of a mile. It measures long distances, such as the length of a road race or the distance between towns. To change kilometers to meters, multiply by 1,000: 3 km is 3,000 m.Measurement · Grade 4, Grade 5, Grade 6SideA side is one of the straight line segments that form the outline of a polygon. Two sides meet at each corner, or vertex. A triangle has 3 sides and a square has 4, and adding the lengths of all the sides gives the perimeter.Geometry · Kindergarten, Grade 1, Grade 2InchAn inch is a US customary unit of length equal to one twelfth of a foot, about the width of an adult thumb. Its abbreviation is in. Rulers split each inch into halves, quarters, eighths and sixteenths. One inch is exactly 2.54 centimeters, and 12 inches make 1 foot.Measurement · Grade 2, Grade 3, Grade 4CentimeterA centimeter is a metric unit of length equal to one hundredth of a meter, about the width of a fingernail. Its symbol is cm. There are 100 centimeters in 1 meter and 10 millimeters in 1 centimeter, and 1 inch equals 2.54 centimeters.Measurement · Grade 3, Grade 4, Grade 5Unit ConversionUnit conversion is rewriting a measurement in a different unit without changing the amount, such as writing 3 feet as 36 inches. You multiply by a conversion factor, a fraction equal to 1 such as 12 in1 ft. Converting to a smaller unit gives a larger number; converting to a larger unit gives a smaller number.Measurement · Grade 4, Grade 5, Grade 6DecimalA decimal is a number written with a decimal point to show parts of a whole. Decimals use place value to represent tenths, hundredths, thousandths and more: in 3.14, the 1 means 1 tenth and the 4 means 4 hundredths. So 0.75 = 75100, and 0.5 is one half.Number System · Grade 4, Grade 5, Grade 6Place ValuePlace value is the value of a digit based on its position in a number. In 3,507 the 5 is worth 500, because it sits in the hundreds place. Each place is worth 10 times the place to its right: ones, tens, hundreds, thousands, and after the decimal point, tenths and hundredths.Number System · Grade 3, Grade 4, Grade 5Scientific NotationScientific notation writes a number as a value from 1 to less than 10 times a power of 10, such as 5.4 × 103 for 5,400. The exponent records how far the decimal point moved: positive for large numbers and negative for numbers between 0 and 1, as in 0.0062 = 6.2 × 10−3.Number System · Grade 8, Algebra 1