Dr. Carmen E. Rexach
THE METRIC SYSTEM
REVIEW
THE METRIC SYSTEM
A quick (and easy!!) way to do metric conversions.
1 meter (M)
1 centimeter (cm)
1 millimeter (mm)
1 micrometer (μm)
1 nanometer (nm)
1 angstrom (A)
0
10
10-2
10-3
10-6
10-9
10-10
1
0.01
0.001
0.000001
0.000000001
0.0000000001
approximates
one yard
1 cm = 1/2 inch
width of pin head
bacteria
virus
width of cell
membrane
To convert within the metric system, follow the steps below!
Example: convert 223.4 cm to nm
1. Write down the exponents.
cm = 10-2 = 2
nm = 10-9 = 9
2. Subtract the exponents
9-2 = 7 This is the number of spaces you will move the decimal.
3. Determine which way to move the decimal
a. You are converting cm to nm, cm =2 to nm =9
b. Move the decimal in the direction of the larger number, in this case,
the 9 (to the right)
4. GO FOR IT!!!
In our example, we will move the decimal 7 spaces to the right.
223.40000000 = 2234000000 nm
Dr. Carmen E. Rexach
5. One more step….let’s restate this number in scientific notation.
?
__.____ x 10
= 2.234 x 109
a. You count the number of spaces the decimal must move to be
placed behind the first number.
b. If the original number (2234000000) is > 1, the exponent is
positive, as in our example.
c. If the original number is <1, the exponent is negative.
Let’s try another one!
Convert 0.004 μm to dm
1. Write down the exponents.
μm = 10-6 = 6
dm = 10-1 = 1
2. Subtract the exponents.
6-1 = 5 This is the number of spaces you will move the decimal.
3. Determine which way to move the decimal.
a. You are converting μm to dm, μm = 6 to dm = 1
b. Move the decimal in the direction of the larger number, in this
case, the 6 (to the left)
In this example, you will move the decimal 5 spaces to the left.
4. GO FOR IT!!
00000.004 = 0.00000004 dm
5. One more step….let’s restate this number in scientific notation.
?
__.____ x 10
= 4.0 x 10-8
Dr. Carmen E. Rexach
d. You count the number of spaces the decimal must move to be
placed behind the first number.
e. If the original number is > 1, the exponent is positive.
f. If the original number is <1, as in our example (0.00000004) the
exponent is negative.
Try the following practice problems. Don’t cut corners! Complete each step
in sequence to arrive at the correct answer.
1. 32.4 A to mm
2. 65 cm to mm
3. 0.003 mm to m
Answers to metric
1. 3.2 x 10 –6 mm
2. 6.5 x 102 mm
3. 3.0 x 10-6 m
4. 1.2 x 10 –3 mm
5. 1.4 x 10 –3 mm
6. 1.8 x 10 3 cm
problems:
(0.00000324 mm)
(650 mm)
(0.000003 m)
(0.001233 mm)
(0.00144 mm )
(1800 cm)
4. 1233 nm to mm
5. 1.44 μm to mm
6. 18 m to cm