UNIT CONVERSION: DIMENSIONAL ANALYSIS

Keke is making beef tinaktak. Her recipe calls for 900 grams of beef. She looks in the refrigerator and sees that she has 1.5 kilograms of beef wrapped in a package. Keke isn’t sure how much of the beef she should use. Does Keke have enough beef for her recipe?

Try This Out

SI PREFIX CONVERSION1. Find the difference between the exponents of the two prefixes.2. Move the decimal that many places.

SI Prefixes

Prefix Scientific notation Meaning

mega (M) 106 1 000 000

kilo (k) 103 1 000

hecto (h) 102 100

deka (da) 101 10

Base Unit 100 1

deci (d) 10-1 0.1

centi (c) 10-2 0.01

milli (m) 10-3 0.001

micro (µ) 10-6 0.000 001

nano (n) 10-9 0.000 000 001

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§ Ex:§ How many mL are in 0.032 L?

§ 0.032 L = _____ mL§ 0.032 L = 32 mL

You Try!§ a) 20 cm = ____ m

§ 0.2 m§ b) 805 dm = ____ km

§ 0.0805 km§ c) 0.177 L = ____ mL

§ 177 mL

0.032 L00.32 L

003.2 L0032. L

12

3

CONVERSION FACTORS

§ Conversion factor: a ratio from the equality between two different units that can be converted from one unit to the other§ Ex: 1 dollar = 4 quarters

Can be written as:4 quarters

1 dollar or 1 dollar4 quarters

§ You can convert factors if you know the relationship between the unit you have and the unit you want! J

You Try!§ Write the conversion factor for 1000 gram = 1 kilogram

§1000 g

1 kg or 1 kg1000 g

If we know an equality relating two units, then we can make 2

conversion factors!

DIMENSIONAL ANALYSIS§ The “Factor-Label” Method

§ Units are canceled (or “factored”) out

§ Steps:1. Identify starting and ending units.2. Line up conversion factors so units cancel out.3. Multiply all top numbers & divide by each bottom number.4. Check units & answer.

=´ 33

cmgcm g

Sample ProblemHow many quarters in 4 dollars?1. Identify starting and ending units.

Given: 4 dollarsUnknown: ? quarters

2. Line up conversion factors so units cancel out.Conversion factor: 1 dollar = 4 quarters4 dollars 4 quarters

1 dollar3. Multiply all top numbers & divide by each bottom number.

4 dollars 4 quarters1 dollar = 16 quarters

4. Check units & answer.

Always start with your given!

Sample Problem: Metric ConversionHow many centigrams are in 23 grams?§Given: 23 g§Unknown: ? cg

§Conversion factor(s): 1 cg = 0.01 g23 g × 1 cg

0.01 g =

= 2300 cg

Use the metric prefix meaning chart to get

your equalities!