elliebomb13
contestada

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

Respuesta :

gmany

[tex]1\ m=1,000\ mm\\\\therefore\\\\5.09\cdot10^{-4}\ mm=5.09\cdot10^{-4}\ mm\div1000\dfrac{mm}{m}\\\\=5.09\cdot10^{-4}\ mm\cdot\dfrac{1}{1000}\ \dfrac{m}{mm}=5.09\cdot10^{-4}\cdot\dfrac{1}{10^3}\ m=5.09\cdot10^{-4}\cdot10^{-3}\ m\\\\=5.09\cdot10^{-4+(-7)}\ =5.09\cdot10^{-7}\ m[/tex]

Answer: C.

Shorter solution:

[tex]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[/tex]