Change Unit (Measure)

How to change the unit of measurement: 3 examples and their solutions.

Example 1

Example

Solution

First write (3 m).

To remove the unit [meters],
you need [meter] in the denominator.
And you need the unit [centimeters] in the numerator.

1 m = 100 cm

So multiply [100 cm]/[1 m].

Cancel the [meter(s)] units.

(3)⋅(100 cm)/1 = 300 cm

So 300 cm is the answer.

Example 2

Example

Solution

First write (2 hr).

To remove the unit [hours],
you need [hour] in the denominator.
And you need the unit [seconds] in the numerator.

1 hr = 60 min
This doesn't show [seconds].
But use this to remove [hours] first.

So multiply [60 min]/[1 hr].

Next, to remove the unit [minutes],
you need [minutes] in the denominator.
And you still need the unit [seconds] in the numerator.

1 min = 60 sec

Use this to remove [minutes] and write [seconds].

So multiply [60 sec]/[1 min].

Cancel the [hour(s)] units.
And cancel the [minute(s)] units.

(2)⋅(60/1)⋅(60 sec)/1 = 7200 sec

So 7200 sec is the answer.

Example 3

Example

Solution

36km/h means 36km per 1 hour.
So write (36 km)/(1 hr).

First, remove the unit [kilometers].
You need [kilometer] in the denominator.
And you need the unit [meter] in the numerator.

1 km = 1000 m

So multiply [1000 m]/[1 km].

Next, remove the unit [hours].
you need [hour] in the numerator.
And you need the unit [seconds] in the denominator.

1 hr = 60 min
This doesn't show [seconds].
But use this to remove [hours].

So multiply [1 hr]/[60 min].

To remove the unit [minutes],
you need [minutes] in the numerator.
And you still need the unit [seconds] in the denominator.

1 min = 60 sec

Use this to remove [minutes] and write [seconds].

So multiply [1 min]/[60 sec].

Solve these ratios by cancelling.

Cancel the [kilometer(s)] units.
Cancel the [hour(s)] units.
And cancel the [minute(s)] units.

(36/1)⋅(1000 m / 1)⋅(1/60)⋅(1/60 sec) = (10 m)/(1 sec) = 10 m/s

So 10m/s is the answer.