What is (5 -2) to the left 3 units?

Answer 1

Here are the necessary conversions:

1 ft = 12 in

1 in = 2.54 cm

1 m = 100 cm

When using conversions like these, you need to make sure that the units you start with get canceled out, so the units you started with need to be in the denominator (bottom of the fraction) in your conversion factor.

So we have the conversion factors*:

1 = 12 in/ft

1 = 2.54 cm/in

1 = 1/100 m/cm = .01 m/cm

(cm in denominator because previous step left us with cm)

Notice that conversion factors equal 1. So when we multiply what we were given by a conversion factor, we aren't changing the value, just the units.

4 ft 8 in = 4 ft * (12 in/ft) + 8 in = 4 * 12 in + 8 in = 48 in + 8 in = 56 in

56 in = 56 in * (2.54 cm/in) = 142.24 cm

142.24 cm = 142.24 cm * (.01 m/cm) = 1.4224 m

so,

4 ft 8 in = 1.4224 m

---- * NOTE: Using conversion factors in this problem was pretty straightforward but what if your conversion didn't have a 1 on one side? Or, what if you were converting in the other direction?

EX: 55 mi = 88 km (which I remember from speed limit signs in Canada)

If we divide both sides by 11, we get: 5 mi = 8 km

There 2 sets of conversion factors, depending on what units you're given:

If given mi: 1 = 8 km / 5 mi = 8/5 km/mi

If given km: 1 = 5 mi / 8 km = 5/8 mi/km

So now we can solve both types of questions:

How many kilometers in 15 miles?

15 mi = 15 mi * (8 km / 5 mi) = 3 * 8 km = 24 km

How many miles in 16 kilometers?

16 km = 16 km * (5 mi / 8 km) = 2 * 5 mi = 10 mi