Question

Write the conversion factors for each: cm/minute to in/second, km/h^2 to m/second^2, and mm^3 to cm^3?

Answer 1

`"1 cm/min = 0.006 56 in/s; 1 km/h"^2 = 7.72 × 10^"-5"color(white)(l) "m/s"^2; "1 mm"^3 = "0.001 cm"^3`

Explanation:

`"cm/min"` to `"in/s"`

`(1 color(red)(cancel(color(black)("cm"))))/(1 color(red)(cancel(color(black)("min")))) × ("1 in")/(2.54 color(red)(cancel(color(black)("cm")))) × (1 color(red)(cancel(color(black)("min"))))/("60 s") = "0.006 56 in/s"`

`"km/h"^2` to `"m/s"^2`

`(1 color(red)(cancel(color(black)("km"))))/(1 color(red)(cancel(color(black)("h"^2)))) × ("1000 m")/(1 color(red)(cancel(color(black)("km")))) × ((1 color(red)(cancel(color(black)("h"))))/("3600 s"))^2 = 7.72 × 10^"-5"color(white)(l) "m/s"^2`

`"mm"^3` to `"cm"^3`

`1 color(red)(cancel(color(black)("mm"^3))) × (("1 cm")/(10color(red)(cancel(color(black)("mm")))))^3 = "0.001 cm"^3`