Metric System
Introduction
The Metric System was designed to have a consistent method of
converting between units. All the units use the same prefixes. In
addition, conversions between different units was simplified as much as
possible. This makes the Metric System much easier to use than the
English, Imperial, System.
|
Metric
System Prefixes
|
|
Mega |
M |
1,000,000 |
106 |
|
kilo |
k |
1,000 |
103 |
|
hecto |
h |
100 |
102 |
|
deka |
da |
10 |
101 |
|
NO PREFIX |
1 |
100 |
|
deci |
d |
0.1 |
10 -1 |
|
centi |
c |
0.01 |
10
-2 |
|
milli |
m |
0.001 |
10
-3 |
|
micro |
|
0.000,001 |
10
-6 |
|
nano
|
n
|
0.000,000,001
|
10-9
|
There are additional prefixes at the end and the beginning of the this
list. The process is the same as you use additional prefixes. It is
convenient to create the chart below. Metric
System Chart
|
106 |
105 |
104 |
103 |
102 |
101 |
100 |
10 -1 |
10 -2 |
10 -3 |
10 -4 |
10 -5 |
10 -6 |
10 -7 |
10-8 |
10 -9 |
|
M |
-- |
-- |
k |
h |
da |
NO |
d |
c |
m |
-- |
-- |
|
-- |
-- |
n |
Procedure
|
| 1. |
Count the
number of times you move from the prefix on the left to prefix on the
right.
|
| 2. |
1 of prefix on
left of chart = 1(number of spaces 0's) on prefix on right of chart.
|
| 3. |
Multiply to
cancel units.
|
| 4. |
If using
exponential notation, 1 of prefix on left = 1 x 10 power(number
on spaces) prefix on right. |
5430 mg = ______________ hg
1 hg = 100,000
mg
1 hg
5430 mg x ------------------ = 0.0543 hg
100,000 mg |
[Move
5 steps from h to m]
mg must go on the bottom part of the fraction
to cancel the mg of 5430 mg. The desired unit must go on the
top. The equality determines which numbers go with the units.
The answer must be smaller by 5 decimal
places. |
5430 hg = _____________ mg
1 hg = 100,000 mg
100,000 mg
5430 hg x ------------------ = 543,000,000 mg
1 hg |
[Move 5 steps from h
to m]
hg must go on the bottom part of the fraction
to cancel the hg of 5430 hg. The desired unit must go on the
top. The equalilty determines which numbers go with the units.
The answer must be larger by 5 decimal places. |
Remember: When you divide by numbers greater than 1, the answer must get
smaller. When you multiply by numbers greater than 1, the answer must get
larger.
When you are multiplying or dividing by multiples of ten, you just move
the decimal point.
Table of Contents
Metric Problems
Convert the
following:
|
|
1.
|
a. |
58,500,000
cg = ____________________ kg |
|
|
b. |
0.000,000,045,8
daL = ____________________ cL |
|
|
c. |
8456 mm =
____________________ m |
|
|
d. |
0.000,000,690
nm = ____________________ cm |
|
|
e. |
1,111,000 dg = ____________________ Mg |
|
|
f. |
85,000 L = ____________________ daL |
|
|
g. |
0.00214 dm =
____________________ nm |
|
|
|
|
|
2.
|
a. |
5.140 x 10-5 m =
____________________ Mm |
|
|
b. |
2.78 x 104
nm = ____________________ km |
|
|
c. |
1.4 x 10-11
hg = ____________________ mg |
|
|
d. |
6.67 x 106
kL = ____________________ cL |
|
|
e.
|
8 x 10-8
hg = ____________________ kg
|
Table of Contents
Metric Answers
Convert
the following:
Metric System Chart |
| 1. |
a. |
58,500,000
cg = ____________________ kg
|
| |
|
1
kg = 100,000 cg
1 kg
58,500,000 cg x ----------------- = 585 kg
100,000 cg |
Move
5 blocks from k to c
100,000 cg goes on the
bottom to cancel the units of 58,500,000 cg.
1 kg must go on the
top because it is the desired unit.
The answer must get
smaller by 5 decimal places. |
|
|
|
|
b. |
0.000,000,045,8
daL = ____________________ cL
|
|
|
1
daL = 10,000 cL
10,000 cL
0.000,000,045,8 daL x --------------- = 0.000,458 cL
1 daL |
Move
4 places from da to c
1 daL goes on the
bottom to cancel the unit of 0.000,000,045,8 daL.
10,000 cL must go on
the top because it is the desired unit.
The answer must get
larger by 4 decimal places. |
|
|
|
|
c. |
8456
mm = ____________________ m
|
|
|
1
m = 1000 mm
1 m
8456 mm x -------------- = 8.456 m
1000 mm |
Move
3 places from no prefix to m
1000 mm goes on the
bottom to cancel the unit of 8456 mm.
1 m must go on the top
because it is the desired unit.
The answer must get
smaller by 3 decimal places. |
|
|
|
|
d. |
0.000,000,690
nm = ____________________ cm
|
|
|
1
cm = 10,000,000 nm
1 cm
0.000,000,690 nm x -----------------------
10,000,000 nm
=
0.000,000,000,000,069,0 cm |
Move
7 places from c to n
10,000,000 nm goes on
the bottom to cancel the unit of 0.000,000,690 nm.
1 cm must go on the
top because it is the desired unit.
The answer must get
smaller by 7 decimal places. |
|
|
|
|
e. |
1,111,000
dg = ____________________ Mg
|
|
|
1
Mg = 10,000,000 dg
1 Mg
1,111,000 dg x --------------------
10,000,000 dg
= 0.1111 Mg
|
Move
7 places from M to d
10,000,000 dg goes on the bottom to cancel the
unit of 1,111,000 dg.
1 Mg must go on the top because it is the
desired unit.
The answer must get smaller by 7 decimal
places.
|
|
|
|
|
f. |
85,000
L = ____________________ daL
|
|
|
1
daL = 10 L
1 daL
85,000 L x ---------- = 8500 daL
10 L
|
Move
1 place from da to NO PREFIX
10 L goes on the bottom to cancel the unit of
85,000 L
1 daL must go on the top because it is the
desired unit
The answer must get smaller by 1 decimal
place.
|
|
|
|
|
g. |
0.00214
dm = ____________________ nm
|
|
|
1
dm = 100,000,000 nm
100,000,000 nm
0.00214 dm x -----------------------
1 dm
= 214,000 nm
|
Move
8 places from d to n
1 dm goes on the bottom to cancel the unit of
0.00214 dm.
100,000,000 nm must go on the top because it
is the desired unit.
The answer must get larger by 8 decimal
places.
|
| |
|
|
| 2. |
a. |
5.140
x 10-5 m = ____________________ Mm
|
|
|
1Mm
= 10 6 m
1 Mm
5.140 x 10 -5 m x -----------
10 6 m
= 5.140 x 10 -11
Mm
|
Move
6 places from M to NO PREFIX
10 6 m must go on the bottom to
cancel the unit of
5.140 x 10 -5 m.
1 Mm must go on the top because it is the
desired unit.
When dividing by a power of ten, subtract the
bottom exponent.
-5 - 6 = - 11
|
|
|
|
|
b. |
2.78
x 104 nm = ____________________ km
|
|
|
1
km = 10 12 nm
1 km
2.78 x 10 4 nm x ----------
10 12 nm
= 2.78 x 10 -8
km
|
Move
12 places from k to n
10 12 nm must go on the bottom to
cancel the unit of 2.78 x 10 4nm.
1 km must go on the top because it is the
desired unit.
When dividing by a power of 10, subtract the
bottom exponent.
4 - 12 = -8
|
|
|
|
|
c. |
1.4
x 10-11 hg = ____________________ mg
|
|
|
1
hg = 10 5 mg
10 5 mg
1.4 x 10 -11 hg x -----------
1 hg
= 1.4 x 10 -6
mg
|
Move
5 places from h to m
1 hg must be on the bottom to cancel the unit
of 1.4 x 10 -11hg.
10 5 mg must go on the top because
it is the desired unit.
When multiplying by a power of 10, add the
exponent.
-11 + 5 = - 6
|
|
|
|
|
d. |
6.67
x 106 kL = ____________________ cL
|
|
|
1
KL = 10 5 cL
10 5 cL
6.67 x 10 6 kL x ----------
1 kL
= 6.67 x 10 11
cL
|
Move
5 places from k to c.
1 kL must go on the bottom to cancel the unit
of 6.67 x 10 6kL
10 5 cL must go on the top because
it is the desired unit.
When multiplying by a power of 10, add the
exponent.
6 + 5 = 11
|
|
|
|
|
e. |
8
x 10-8 hg = ____________________ kg
|
|
|
1
kg = 10 1 hg
1 kg
8 x 10 -8 hg x ----------- = 8 x 10 -9 kg
10 1 hg
|
Move
1 place from k to h.
10 1 hg must go on the bottom to
cancel the unit of 8 x 10 -8 hg.
1 kg must go on the bottom because it is the
desired unit.
When dividing by a power of 10, subtract the
bottom exponent.
-8 - 1 = - 9
|
Table of Contents
|
