AI Tutor
A single grain of sand weighs about 1 milligram1\text{ milligram}, a dollar bill weighs 1 gram1\text{ gram}, and a bag of flour weighs 1 kilogram1\text{ kilogram}.
The metric system uses prefixes based on powers of 1010 to measure everything from tiny specks of dust to giant sacks of grain.

The Mass Staircase

Mass measures the amount of matter in an object, using the gram (g\text{g}) as its base unit.
A decagram (dag\text{dag}) equals 10 grams10\text{ grams}, a kilogram (kg\text{kg}) equals 1,000 grams1{,}000\text{ grams}, and a milligram (mg\text{mg}) is just 11,000\frac{1}{1{,}000} of a gram.
How do we switch between these units when measuring ingredients or science lab samples?

Converting Big to Small

When converting from a larger unit to a smaller unit, you multiply by powers of 1010 because it takes many small pieces to equal one large piece.
Let's convert 4.5 dag4.5\text{ dag} into milligrams (mg\text{mg}). Since 1 dag=10 g1\text{ dag} = 10\text{ g} and 1 g=1,000 mg1\text{ g} = 1{,}000\text{ mg}, there are 10×1,000=10,000 mg10 \times 1{,}000 = 10{,}000\text{ mg} in 1 dag1\text{ dag}.
4.5×10,000=45,000 mg4.5 \times 10{,}000 = 45{,}000\text{ mg}
What if we need to go in reverse, turning tiny milligrams into kilograms?

Converting Small to Big