Conversion Factors: Additional Practice (Set 2)

Square meters hides two lengths, so square the length factor.

$3 \text{ m}^2 \times \left(\dfrac{100 \text{ cm}}{1 \text{ m}}\right)^2 = 3 \times 10000 = 30000 \text{ cm}^2$

So $3$ square meters is $30000$ square centimeters.

Square yards hides two lengths, so square the length factor.

$5 \text{ yd}^2 \times \left(\dfrac{3 \text{ ft}}{1 \text{ yd}}\right)^2 = 5 \times 9 = 45 \text{ ft}^2$

So $5$ square yards is $45$ square feet.

Cubic meters hides three lengths, so cube the length factor.

$2 \text{ m}^3 \times \left(\dfrac{100 \text{ cm}}{1 \text{ m}}\right)^3 = 2 \times 1000000 = 2000000 \text{ cm}^3$

So $2$ cubic meters is $2{,}000{,}000$ cubic centimeters.

Liters should cancel, so put liters in the denominator of the factor.

$3 \text{ L} \times \dfrac{1000 \text{ cm}^3}{1 \text{ L}} = 3 \times 1000 = 3000 \text{ cm}^3$

So $3$ liters is $3000$ cubic centimeters.

One hour is $3600$ seconds, so multiply the per-second count by those $3600$ seconds. The seconds cancel, leaving a total number of bottles.

$\dfrac{3 \text{ bottles}}{1 \text{ s}} \times 3600 \text{ s} = 3 \times 3600 = 10800 \text{ bottles}$

So the machine fills $10800$ bottles in one hour.

Convert meters to kilometers on top and seconds to hours on the bottom, flipping the second factor.

$\dfrac{15 \text{ m}}{1 \text{ s}} \times \dfrac{1 \text{ km}}{1000 \text{ m}} \times \dfrac{3600 \text{ s}}{1 \text{ h}} = \dfrac{15 \times 3600}{1000} = 54 \text{ km/h}$

So $15$ meters per second is $54$ kilometers per hour.

Convert meters to kilometers on top and seconds to hours on the bottom, flipping the second factor.

$\dfrac{2 \text{ m}}{1 \text{ s}} \times \dfrac{1 \text{ km}}{1000 \text{ m}} \times \dfrac{3600 \text{ s}}{1 \text{ h}} = \dfrac{2 \times 3600}{1000} = 7.2 \text{ km/h}$

So $2$ meters per second is $7.2$ kilometers per hour.

Liters should cancel, so put liters in the denominator.

$2.5 \text{ L} \times \dfrac{1000 \text{ mL}}{1 \text{ L}} = 2.5 \times 1000 = 2500 \text{ mL}$

So $2.5$ liters is $2500$ milliliters.

Square centimeters hides two lengths, so square the length factor.

$5 \text{ cm}^2 \times \left(\dfrac{10 \text{ mm}}{1 \text{ cm}}\right)^2 = 5 \times 100 = 500 \text{ mm}^2$

So $5$ square centimeters is $500$ square millimeters.

Cubic yards hides three lengths, so cube the length factor.

$5 \text{ yd}^3 \times \left(\dfrac{3 \text{ ft}}{1 \text{ yd}}\right)^3 = 5 \times 27 = 135 \text{ ft}^3$

So $5$ cubic yards is $135$ cubic feet.

Convert miles to feet on top and hours to seconds on the bottom, flipping the time factor.

$\dfrac{30 \text{ mi}}{1 \text{ h}} \times \dfrac{5280 \text{ ft}}{1 \text{ mi}} \times \dfrac{1 \text{ h}}{3600 \text{ s}} = \dfrac{30 \times 5280}{3600} = 44 \text{ ft/s}$

So $30$ miles per hour is $44$ feet per second.

Convert feet to miles on top and seconds to hours on the bottom, flipping the second factor.

$\dfrac{22 \text{ ft}}{1 \text{ s}} \times \dfrac{1 \text{ mi}}{5280 \text{ ft}} \times \dfrac{3600 \text{ s}}{1 \text{ h}} = \dfrac{22 \times 3600}{5280} = 15 \text{ mph}$

So the cyclist rides $15$ miles per hour.