Writing Equivalents with Whole Numbers

It's easier to picture the relationship between two units when you use the equivalent with whole numbers, i.e. no fractions or decimals.

I'll now rewrite some equivalents from Table in previous lesson to make them easier.

Which metric equivalents use whole numbers?
The ones for prefix units larger than the root unit.
Because they all involve positive powers of 10, which are always greater than 1.
These equivalents are fine as is.

Which metric equivalents have fractions in them?
The ones for prefix units smaller than the root unit.
Because they all involve negative powers of 10, which are always fractions between 0 and 1.
We'll rewrite these equivalents.

Example 1: Write the Two Equivalents for Meters (m) and Centimeters (cm)
Centimeters are smaller than the root unit meters.
Look at Table in previous lesson and see that the equivalent given is 1 cm = 10-2 m.

Remember that this means 1 cm = 1/100 m.
In other words a cm is a hundredth of a meter.

But if a cm is a hundredth of a meter, then 100 of them must fit in a meter.
In other words, 1 m = 100 cm
Which is: 1 m = 102 cm.

So the two equivalents are:

Example 2: Write the Two Equivalents for Kilograms (kg) and Grams (g)
(A kilogram is a larger unit than the root unit gram.)

Look at Table in previous lesson and see the equivalent 1 km = 103 m.
Substitute the root unit grams for the root unit meters and re-write this as 1 kg = 103 g

Remember that this means 1 kg = 1000 g.

But if a kg is a thousand grams, then each gram must be a thousandth of a kg.
In other words, 1 g = 1/1000 kg
Which is: 1 g = 10-3 Kg

So the two equivalents are:

So using the metric equivalents with whole numbers means:
Always use the metric equivalent in which
1) the bigger unit is set to 1 and
2) the smaller units are a positive power of 10.

The table below is the same as table in previous lesson except that:
1) It shows the easiest equivalents to use for each unit., and
2) The powers of 10 that have no unit names are left out.

 Table The Easiest Equivalents to Use for Converting Some Metric Units Unit Equivalent from Table 21 in which 1 "prefix unit" = this many root units Easiest to Use Equivalent in which 1 bigger unit = this many smaller units Mm 1 Mm = 106 m 1 Mm = 106 m Notice that for prefix units larger than the root unit, we didn't have to change the equivalents in the two columns km 1 km = 103 m 1 km = 103 m hm 1 hm = 102 m 1 hm = 102 m dam 1 dam = 101 m 1 dam = 101 m root unit, i.e. meter (m), gram (g), or liter (L) dm 1 dm = 10-1 m 1 m = 101 dm Notice that for prefix units smaller than the root unit, we rewrote the equivalents so that the bigger unit is set equal to 1 cm 1 cm = 10-2 m 1 m = 102 cm mm 1 mm = 10-3 m 1 m = 103 mm m 1 m = 10-6 m 1 m = 106 m
People who saw this lesson also found the following lessons useful:
 Converting Metric Units into Another Metric Units Writing Equivalents How to Convert Metric Units Creating Conversion Factor from Equivalent Master Metric Equivalent and Conversion Factor How Numbers Behave When Multiplied or Divided by Positive Powers of Ten To Convert Between Two Prefix Units The shortcut for converting metric units

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