# Dimensional Analysis and Metric Conversions

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```					Dimensional Analysis and
Metric Conversions
SC Standards

PS-1.5
Organize and interpret the data
from a controlled scientific
investigation by using mathematics
(including formulas and dimensional
analysis), graphs, models, and/or
technology.
Dimensional Analysis
Conversion factors:
•using ratios of equivalent values to
convert from one unit of measure to
another.

1 gram = 1000 milligrams

1g             or      1000 mg
1000 mg                     1g
60 sec = 1 min.

60 sec         or       1 min.
1 min.                  60 sec
What would the conversion factors
be for years and days?

365 days       or         1 year
1 year                   365 days
Dimensional Analysis
1.) Write down given number and unit
2.) Write down “x” and a line
3.) Put given unit on side of line so it will
cancel and the desired unit on the other
side (may take more than 1 step)
4.) Fill in appropriate numerical relationship
for the ratio
5.) Multiply the top and divide by the
bottom

…see examples…
• Example #1
–How many seconds are there
in 1 year?

1 year x 365 days x 24hr x _____ x 60 sec.
_____      ____ 60min. _____
1year     1day 1 hr       1 min

= 31,536,000 sec.
Example #2 - How many inches are
there in 85.6 cm? (1in = 25.4mm)

1 in
10 mm x _____
85.6cm x _____
1 cm   25.4 mm

= 33.7 in.
Example #3 - How many fluid ounces
are there in 2.0 gallons?

(1gall = 4 qts, 1 qt = 2 pints, 1 pint = 2 cups,
1 cup = 8 fl. oz.)

2.0 gall       4 qts x _____
x _____          2 pt
1 gal      1 qt.
2 cup
x _____ x _____ oz.
8 fl.
1 pt.      1 cup
= 256 fl. oz.
Conversion Practice

Kilo

Hecto
Deka

Deci

Centi

Milli
Example #1
How many meters are there
in 48 km?

Khdbdcm

So…move the decimal 3
places to the right
48 km = 48, 000 m
Example #2
– How many decigrams are there in
45, 456 µg

Khdbdcm µ

So…move the decimal 5 places
to the left
45,456 µg = 0.45456 dg
Practice
• 100 mg = ___g   • 109g = ___ kg

• 160 cm = __mm   • 250m = ___Hm

• 1 L = ____mL    • 56 cm = ___m

• 14 km = ___m    • 7 g = ___mg
Practice
• 100 mg = 0.1g    • 109g = 0.109kg

• 160cm=1600mm     • 250m = 2.50Hm

• 1 L = 1000 mL    • 56 cm = 0.56 m

• 14 km = 14000m   • 7 g = 7000 mg

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