Lesson 4: Use exponents to denote powers of 10 with application to metric conversions.

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

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

Explanation

Metric prefixes are essentially built-in scientific notation shortcuts! The prefix 'kilo-' literally means 10^3 (one thousand). When converting, just remember: switching to a smaller unit means you will need more of them to cover the same distance/weight, so you multiply. Switching to a larger unit means you need fewer of them, so you divide.