Zeta Instruction Manual
Copyright 2012
Lesson 8 - illustrating a
significant expansion
of content
LESSON 8
Metric System Conversion–Part 1
In the last two lessons you learned the meaning of these metric prefixes, as well as
their abbreviations.
kilo (k) = 1,000
hecto (h) = 100
deka (da) = 10
deci (d) =
1
10
centi (c) =
1
100
milli (m) =
1
1,000
You have also been writing these relationships as ratios in tables like these:
Figure 1
1 kilounit 1 hectounit 1 dekaunit 1 unit 1 deciunits
1,000 units
100 units
10 units
1 unit
1
unit
10
1 centiunits
1 milliunits
1
unit
100
1
unit
1,000
1 kilounit 1 hectounit 1 dekaunit 1 unit 10 deciunits 100 centiunits 1,000 milliunits
1,000 units
100 units
10 units
1 unit
1 unit
1 unit
1 unit
METRIC SYSTEM CONVERSION–PART 1 - LESSON 8
37
In this lesson you will use these ratios as multiplication factors to convert larger
units to smaller units. You will first learn the standard method, which involves
multiplying by conversion ratios, and then we will look at an alternative method
and a shortcut.
Method 1 (Standard Method)
The standard way of converting units using a ratio is to multiply the original
unit by the appropriate ratio. For example if you need to convert one kilogram to
grams, you multiply by the ratio which shows the relationship between kilograms
and grams. Because the amounts on the top and bottom of these ratios are the
same, you can present each ratio either way without changing the value.
Figure 2
1 kilogram (kg)
1,000 grams (g)
=
1,000 grams (g)
1 kilogram (kg)
When choosing which ratio to multiply by, you will need to arrange it so that
the unit you are converting to is on top.
Example 1
1 kilogram (kg) ×
1,000 m
1 kilogram (kg)
= 1,000 grams (g)
Notice that you can cancel the unit kilograms because we are dividing kilograms
by kilograms, and because of this you will end up with an answer in grams. Also
notice that when converting kilograms to grams you ended up multiplying by
1,000 which is exactly what "kilo" means.
It becomes slightly more complicated when you convert from one unit that has
a prefix to another unit which has a prefix. For example, if you convert 1 kilometer
to centimeters it requires two of the conversion ratios as factors.
Example 2
1 km
×
1,000 m
1 km
×
100 cm
= 1(1,000)(100 cm) = 1,000,000 cm
1 m
If you start with a number of units other than one, you just multiply that
number by each factor along the way.
38
LESSON 8 - METRIC SYSTEM CONVERSION–PART 1
ZETA
Example 3
×
15 hl
100 L
×
10 dl
= 15(100)(10)dl = 15,000 dl
1 L
1 hl
If you need to convert between two units that are close to each other in size,
you may end up both multiplying and dividing. For example if you use the ratios
to convert one centiliter to milliliters it looks like this.
Example 4
×
1 cl
1 L
10 cl
×
1,000 ml
= 10 ml
1 L
Method 2 (Alternative Method)
Think about the way conversions like this interact with place value. When you
go from tens to hundreds you multiply by 10, and when you go from hundreds to
thousands you multiply by 10 again. Because of this, if you create a ratio between
any two units that are next to each other on our original table, you can describe
them as a ratio of 10 to 1.
Figure 3
10 hectounits 10 dekaunits
1 kilounit
10 units
10 deciunits 10 centiunits 10 milliunits
1 hectounit 1 dekaunit
1 unit
1 deciunit
1 centiunit
If you are converting between two units that are adjacent to each other, these
10 to 1 ratios can be very helpful.
Example 5
3 km
×
2 cm
×
10 hm
= 30 hm
1 km
10 mm
1 cm
= 20 mm
If you are converting between units that are farther apart, you end up
multiplying by the same ratio several times. You use the ratio once for each step
ZETA
METRIC SYSTEM CONVERSION–PART 1 - LESSON 8
39
that the units were separated by on the original chart. As shown in the video
lesson, this is the same as multiplying by 10 for each step from larger to smaller on
the chart.
Example 6
27 hg
× 10 dag ×
10 g
1 hg
1 dag
10 dg
×
= 27(10)(10)(10) dg = 27,000 dg
1 g
Method 2 Shortcut
Each place in our decimal place value system is 10 times the place before
it. Each metric unit is also 10 times as large as the unit to the right of it on the
chart. Because of this, we are, in effect, adding a zero for each step along the unit
conversion chart as we go from larger to smaller.
In summary, you have now learned two different ways for converting a larger
metric unit to a smaller metric unit.
Example 7 (Method 1)
100 L
32 hl ×
1 hl
×
10 dl
= 32(100)(10) dl = 32,000 dl
1 L
Example 8 (Method 2)
32 hg
× 10 dag
1 hg
×
10 g
×
1 dag
10 dg
= 32(10)(10)(10) dg = 32,000 dg
1 g
Because each step in the alternative method involves multiplying by 10 as you
go from larger to smaller, you can use the shortcut of just changing the place value
of the original number, thus "moving" the decimal place by adding a zero for each
conversion step.
Example 9 (Method 2 Shortcut)
32. → 32000.
When doing the problems in the worksheets, you may use whichever method
works best for you in a given problem.
40
LESSON 8 - METRIC SYSTEM CONVERSION–PART 1
ZETA