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Writing Equivalents with Whole Numbers
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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:
Two Equivalents for Meters (m) and Centimeters (cm)

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:
 Two Equivalents for Kilograms (kg) and Grams (g)

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
mium 1 mium = 10-6 m 1 m = 106 mium
 the smaller units are a positive power of 10.
The table on the next page is the same as Table 10 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.
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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