Short answer: Multiply by 100 for centimeters or 1000 for millimeters.

Long answer:
The metric system makes it easy to convert between different units because the whole system is base ten. As long you remember the names, it becomes easy to convert between them.

kilometer 1000
hectometer 100
decameter 10
meter 1
decimeter 0.1 (rarely used)
centimeter 0.01
millimeter 0.001

Pre-EXAMPLE

When converting units, you can always solve the problem by setting up a proportion. As you become more and more familiar with these types of problems, you’ll start to notice certain patterns. Think about it like this: you know that 4 quarters make up a dollar. When someone asks you how many quarters are in 3 dollars, you pretty quickly know to multiply 3 dollars by 4. Similar patterns happen with metric conversions, but setting up a proportion will never fail you. Here’s what happened in the quarter problem:

1 dollar = 4 quarters

##”1 dollar”/”4 quarters”##= ##”3 dollars”/”x quarters”##

When you cross multiply, you are left with:

##x## = ##12″ quarters”##.

We could have gotten to 12 quarters by multiply 3 dollars by 4 (since there are 4 quarters in a dollar), but setting up a proportion correctly and solving will never fail you!

EXAMPLE 1:

We’re given 32 meters (m) and we’d like to know how many centimeters (cm) that is. Let’s start with what we know:
1 m = 100 cm

We can set up a proportion to solve for the number of centimeters. We are given 3 pieces of information, and asked to find a 4th:

##”1 m”/”100 cm”##= ##”32.7 m”/”x cm”##

Note: Make sure to be consistent with you units (in this case, meters in the numerator and centimeters in the denominator). Otherwise, you will end up with the incorrect answer!

Now, cross multiply to solve for our unknown ##x##:
##x## = ##3,270″ cm”##. Note that our answer here is in cm, the units we want.

After completing a bunch of these problems, you may notice that to convert from meters to centimeters, you simply multiply the meters by 100 (since there are 100 centimeters in 1 meter).

EXAMPLE 2:

We’re given 0.062 meters (m) and we’d like to know how many millimeters (mm) that is. Let’s start with what we know:
1 m = 1,000 mm

Set up your proportion:

##”1 m”/”1,000 mm”##= ##”32.7 m”/”x mm”##

Cross multiply to solve for our unknown ##x##:
##x## = ##32,700″ mm”##

After completing a bunch of these problems, you may notice that to convert from meters to millimeters, you simply multiply the meters by 1000 (since there are 1,000 millimeters in 1 meter).

Easy to read and understand here: https://www.mathsisfun.com/measure/metric-length.html

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