What happens to the numerical value and the unit of a measurement that is multiplied by a conversion factor?

Answer 1

The conversion factor has the effect of multiplying the measurement by 1, thereby not changing the measurement.

Example: you measure 5 inches, and want to convert to millimeters.

Since 1 inch = 25.4 mm (an equality), divide both sides by (1 inch) to get:

(1 inch)/(1 inch) = (25.4 mm)/(1 inch) ---> 1 = 25.4 (mm/inch)

so if you multiply 5 inches by 1, you still have 5 inches.

Multiplying by [25.4 (mm/inch)] is the same as multiplying by one.

Therefore (5 inches) * 1 = (5 inch) * 25.4 (mm/inch) = 127 inch*mm/inch

The 'inches' cancel and you have 5 inches = 127 mm

Some people write it like this to make it easier to cancel the units:

25.4 mm | 5 inch

--------------------- = 127 mm

1 inch |

likewise, if you had used a metric ruler & measured 127 mm instead of inches:

1 inch | 127 mm

----------------------- = 5 inches

25.4mm |

So rather than try to remember if you multiply or divide by 25.4, just look to

see which operation will cancel the units and leave the new desired units.

Answer 2

Typically, the result is expressed as the multiple of the measurements.

Example:

Tom traveled 50 feet in 10 seconds. Therefore, he traveled 5 ft/s.

Answer 3

The numeriacal value and the measurement unit will change. The actual size remains the same.