Metric Conversions Using Powers of 10
Metric prefixes represent powers of 10 relationships to a base unit, so kilo- means 1000, centi- means 1/100, and milli- means 1/1000. To convert to a smaller unit multiply by the power of 10, and to convert to a larger unit divide by the power of 10. This Grade 5 math skill from Eureka Math Chapter 1 covers multiplicative patterns applied to metric measurement conversion.
Key Concepts
Property Metric prefixes represent a power of 10 relationship to a base unit (like meter, gram, or liter). kilo (k) = $10^3$ base units centi (c) = $10^{ 2}$ base units (or 1 base unit = $10^2$ centi units) milli (m) = $10^{ 3}$ base units (or 1 base unit = $10^3$ milli units).
To convert from a larger unit to a smaller unit, multiply by $10^n$. To convert from a smaller unit to a larger unit, divide by $10^n$.
Examples Example 1 (Larger to Smaller): Convert 4.5 meters to centimeters. Since you are converting to a smaller unit, multiply by 10^2. 4.5 m = 4.5 x 10^2 cm = 450 cm Example 2 (Smaller to Larger): Convert 2,300 grams to kilograms. Since you are converting to a larger unit, divide by 10^3. 2,300 g = 2,300 / 10^3 kg = 2.3 kg.
Common Questions
What do metric prefixes mean?
Metric prefixes indicate the power of 10 relationship to the base unit: kilo- means 1000 base units, centi- means 1/100 of a base unit, and milli- means 1/1000 of a base unit.
How do you convert meters to centimeters?
Since centi- means 1/100, there are 100 centimeters in 1 meter. Multiply by 100: 4.5 meters times 100 equals 450 centimeters.
How do you convert grams to kilograms?
Since kilo- means 1000, there are 1000 grams in 1 kilogram. Divide by 1000: 2300 grams divided by 1000 equals 2.3 kilograms.
Why does the number get smaller when converting to a larger metric unit?
When converting to a larger unit you need fewer of them to represent the same amount, so you divide by the power of 10 relationship, which reduces the numerical value.