Question

Which shows the conversion of 5.09 × 10-4 millimeters to meters?

A. 5.09 × 10-4 mm ÷ 10 mm/m = 5.09 × 10-5 m
B. 5.09 × 10-4 mm ÷ 1000 mm/m = 5.09 × 10-6 m
C. 5.09 × 10-4 mm ÷ 1000 mm/m = 5.09 × 10-7 m
D. 5.09 × 10-4 mm ÷ 10,000 mm/m = 5.09 × 10-8 m

Answer 1

`1\ m=1,000\ mm\\\\therefore\\\\5.09\cdot10^(-4)\ mm=5.09\cdot10^(-4)\ mm/1000(mm)/(m)\\\\=5.09\cdot10^(-4)\ mm\cdot(1)/(1000)\ (m)/(mm)=5.09\cdot10^(-4)\cdot(1)/(10^3)\ m=5.09\cdot10^(-4)\cdot10^(-3)\ m\\\\=5.09\cdot10^(-4+(-7))\ =5.09\cdot10^(-7)\ m`

Answer: C.

Shorter solution:

`1\ m=1,000\ mm\to1\ mm=0,001\ m=10^(-3)\ m\\\\5.09\cdot10^(-4)\ mm=5.09\cdot10^(-4)\cdot10^(-3)\ m=5.09\cdot10^(-4+(-3))\ m\\\\=5.09\cdot10^(-7)\ m`