Conversion Factors: Practice

Meters should cancel, so put meters in the denominator of the factor.

$5 \text{ m} \times \dfrac{100 \text{ cm}}{1 \text{ m}} = 5 \times 100 = 500 \text{ cm}$

So $5$ meters is $500$ centimeters.

Multiply by the factor that cancels feet and leaves inches.

$2 \text{ ft} \times \dfrac{12 \text{ in}}{1 \text{ ft}} = 2 \times 12 = 24 \text{ in}$

So the ribbon is $24$ inches long. Adding $12$ to $2$ instead of multiplying gives the wrong answer $14$.

Centimeters should cancel, so put centimeters in the denominator.

$8 \text{ cm} \times \dfrac{10 \text{ mm}}{1 \text{ cm}} = 8 \times 10 = 80 \text{ mm}$

So $8$ centimeters is $80$ millimeters.

To cancel inches, inches must sit in the denominator, and the factor must use the true equality $1 \text{ ft} = 12 \text{ in}$.

$60 \text{ in} \times \dfrac{1 \text{ ft}}{12 \text{ in}} = \dfrac{60}{12} = 5 \text{ ft}$

The factor $\dfrac{12 \text{ ft}}{1 \text{ in}}$ also has inches on the bottom, but it states a false equality, so it is wrong.

Kilometers should cancel, so put kilometers in the denominator.

$7 \text{ km} \times \dfrac{1000 \text{ m}}{1 \text{ km}} = 7 \times 1000 = 7000 \text{ m}$

So $7$ kilometers is $7000$ meters.

Pounds should cancel, so the factor carries pounds in the denominator.

$3 \text{ lb} \times \dfrac{16 \text{ oz}}{1 \text{ lb}} = 3 \times 16 = 48 \text{ oz}$

So $3$ pounds is $48$ ounces.

Minutes should cancel, so put minutes in the denominator.

$5 \text{ min} \times \dfrac{60 \text{ s}}{1 \text{ min}} = 5 \times 60 = 300 \text{ s}$

So $5$ minutes is $300$ seconds.

Dozens should cancel, so the factor has dozens in the denominator.

$4 \text{ dozen} \times \dfrac{12 \text{ eggs}}{1 \text{ dozen}} = 4 \times 12 = 48 \text{ eggs}$

So $4$ dozen is $48$ eggs.

Miles should cancel, so put miles in the denominator.

$2 \text{ mi} \times \dfrac{5280 \text{ ft}}{1 \text{ mi}} = 2 \times 5280 = 10560 \text{ ft}$

So $2$ miles is $10560$ feet.

Meters should cancel, so put meters in the denominator.

$4 \text{ m} \times \dfrac{1000 \text{ mm}}{1 \text{ m}} = 4 \times 1000 = 4000 \text{ mm}$

So $4$ meters is $4000$ millimeters.

Gallons should cancel, so the factor carries gallons in the denominator.

$5 \text{ gal} \times \dfrac{4 \text{ qt}}{1 \text{ gal}} = 5 \times 4 = 20 \text{ qt}$

So $5$ gallons is $20$ quarts.

Feet should cancel, so put feet in the denominator.

$10 \text{ ft} \times \dfrac{12 \text{ in}}{1 \text{ ft}} = 10 \times 12 = 120 \text{ in}$

So $10$ feet is $120$ inches.