Question

Use two unit multipliers to convert 600 miles to inches. ( Do not multiply out.)

Answer 1

Answer:

(600 mi) × (5280 ft/mi) × (12 in/ft)

Step-by-step explanation:

A "unit multiplier" is a multiplier that has a value of 1. That is, the numerator and denominator have the same value. For units conversion problems, the numerator quantity has the units you want, and the denominator quantity has the units you're trying to cancel.

You have units of miles. You know that ...

1 mile = 5280 feet

1 foot = 12 inches

You want to get to units of inches. With these conversion factors, you can do it in two steps (as the problem requests). The first conversion is from miles to feet using the unit multiplier (5280 feet)/(1 mile). This gives you a number of feet.

Then the second conversion is from feet to inches, so you use the one that lets you put inches in the numerator and feet in the denominator:

(12 inches)/(1 foot)

When you multiplie these all out, units of miles and feet cancel, and you're left with inches.

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With the above conversion factors, you can write unit mulipliers of either ...

(5280 ft)/(1 mi) . . . to convert to feet

or

(1 mi)/(5280 ft) . . . to convert to miles.