Measurement - Fundamentals of Chemistry - page 43

EXAMPLE 2.20

Which is bigger—1 Mg or 1 mg?

Solution

1 Mg 1,000,000 g (see Table 2.2)

1 mg 0.001 g

A megagram (Mg), equal to a metric ton, is a billion times larger than a
milligram (mg).

The metric system is easier to use than the English system.

EXAMPLE 2.21

(a) How many meters are in 5.200 km?

(b) How many yards are in 5.200 miles?

Solution

We can use the factor-label method (Section 2.1) to do these metric calculations.

Definition
of kilo-

a 1000 m
1 km

Kilometers Meters

(a) 5.200 km b 5200 m

a 1760 yards
1 mile

(b) 5.200 miles b 9152 yards

Yards
mile

Miles Yards

The metric system problem, part (a), can be solved without paper and pencil—
by moving the decimal point in 5.200 three places to the right. The English sys-
tem conversion, part (b), requires that we remember the number of yards per
mile (harder than the 1000 m/km metric conversion factor) and that we use pen-
cil and paper or a calculator to do the arithmetic. The conversion factor 1000
is used for kilograms, kiloliters, kilowatts, and any other factor involving the
prefix kilo -. The English conversion factor 1760 yd/mile is not used in any other
conversion.

Practice Problem 2.21 (a) How many centimeters are in 2.370 m?
(b) How many inches are in 2.370 ft? (c) For which of these two conversions
do we need to use a calculator?

To convert a value expressed in a primary metric unit to its equivalent in
a subunit, or vice versa, use a conversion factor with a 1 in front of the sub-
unit and the equivalent value in front of the main unit. Note that either the pre-
fix abbreviation or its equivalent is in front of the symbol for the primary unit:

Prefix Equivalent value

Kilo 1000

Centi 0.01

Milli 0.001