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Chapter 3 Metric Units and Conversions

3.1 The Metric System and Prefixes

Metric system: a simple decimal system of measurement that uses the following basic units:

Quantity Basic Unit Symbol

length meter m

mass gram g

volume liter L

time second s

Metric prefixes change the size of the basic unit to larger or smaller units. Each prefix

represents a power of 10.

Know the following metric prefixes!

Prefix Symbol Multiplier

kilo k 1000 times larger

deci d 10 times smaller

centi c 100 times smaller

milli m 1000 times smaller

micro 1,000,000 times smaller

3.2 Metric Conversions

In order to solve conversion problems you need to know how to set up the problem and how to

write conversion factors. When two quantities are equal, you can write them in fraction form as

a conversion factor. For example, 60 seconds equals 1 minute. Thus you can write the two

60 ) or (1 ). Which one you use depends on the given.

conversion factors as (1 60

Fill in the blanks to make the two quantities equal. You must memorize these:

1 m = _________ cm 1 m = _______________ m

1 m = _________ dm 1 m = _______________ mm

1 km = _________ m Note - meters could be grams or liters in these

To remember the number of centimeters or decimeters in a meter, just think of the number of

cents or dimes in a dollar! Note metric conversion factors are all exact.

Smith, Clark (CC-BY-SA 4.0) GCC CHM 130 Chapter 3: Conversions page 1

METRIC-METRIC CONVERSIONS

Factor Label Method: We will use this method for problem solving throughout the semester!

Factor Label Method Steps

1. Identify units for what you want to FIND (answer).

2. Identify the GIVEN (starting point).

3. Multiply GIVEN quantity by 1 or more conversion factors (shown as fractions) so that all

units cancel except the units needed for the final answer. (Include units in your set-up!)

4. Check for correct units and round the final answer to the proper number of sig figs.

It should be noted that you never start with the conversion factor as you do not know yet which

number should be on top! Always start with the GIVEN.

Example 1. How many meters is 4.5 km?

Given: 4.5 km Wanted: ? meters

Conversion Factors: 1000 m = 1 km

4.5 km (1000 ) = 4500 m

1

Example 2. How many m are in 0.0257 cm?

Given: 0.0257 cm Wanted: ? m

Conversion Factors: 100 cm = 1 m, 1,000,000 m = 1 m

1 ) ( 1000,000 ) = 257 m

0.0257 cm (100 1

When performing conversions, SHOW ALL WORK for full points in this class! If your set-up

is correct, then all units cancel except for the final desired units.

Note that exact conversion factors and exact counted values do not limit sig figs. Use sig

fig rules only for measured values (such as 15.8 g) or approximate conversion factors (454

grams = 1 pound is approximate)

3.3 English Conversions

English conversion factors we expect you to know: Note these are all exact.

2 cups = 1 pint 2 pints = 1 quart 4 quarts = 1 gallon

12 inches = 1 foot 3 feet = 1 yard 1760 yards = 1 mile

60 sec = 1 minute 60 min = 1 hour 24 hours = 1 day

Smith, Clark (CC-BY-SA 4.0) GCC CHM 130 Chapter 3: Conversions page 2

Example 1: How many quarts are there if you have 8.25 cups?

Given: 8.25 cups Wanted: ? quarts

Conversion Factor: 2 cups = 1 pint, 2 pints = 1 quart

1 ) (1 ) = 2.06 quarts

8.25 c (2 2

Example 2: How many feet is 39 inches?

Given: 39 inches Wanted: ? feet

Conversion Factor: 12 inches = 1 foot

1 ) = 3.3 feet

39 inches (12

3.4 Metric - English Conversions

To go between the English and Metric systems you need the following conversion factors. These

conversions will be given to you on quizzes and exams:

1 in. 2.54 cm (exact) 1 lb = 454 g (approximate) 1 qt = 946 mL (approximate)

These conversion factors linke the metric system to the English system for lengh, mass, and

volume. Luckily, everyone uses the same units for time.

Example 1: How many mL are in 1.00 pint?

Given: 1.00 pint Wanted: ? mL

Conversion Factor: 2 pints = 1 quart, 1 quart = 946 mL

1.00 pint (1 ) (946 ) = 473 mL

2 1

YouTube Conversion Problem 1

Example 2: How many meters are in a 100.0 yard football field?

Given: 100.0 yards Wanted: ? meters

Conversion Factors: 1 yard = 3 feet, 1 foot = 12 inch, 1 inch = 2.54 cm, 100 cm = 1 m

3 ) (12 ) (2.54 ) ( 1 ) = 91.44 m

100.0 yds (1 1 1 100

Note this answer shows us that yards and meters are NOT equal! 1 m does not equal 1 yard.

Smith, Clark (CC-BY-SA 4.0) GCC CHM 130 Chapter 3: Conversions page 3

What is the conversion 5 g into ML?Since 1 milliliters is equivalent to 1 gram, 5 ml would equal to 5 grams. The 5 Grams to Milliliters converter will not only find out 5 grams equals how many ml, it will also convert 5 grams to other units such as quarts, pint, cup, tablespoon, teaspoon and more.

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