Barrons SAT Subject Test Chemistry, 13th Edition

of the exponents gives 10−7. Now, changing to a number with only one digit to the

left of the decimal point gives you 1.15 × 10−6 for the answer.

Try these:

(5.1 × 10−6)(2 × 10−3) = 10.2 × 10−9 = 1.02 × 10−8

(3 × 10^5 )(6 × 10^3 ) = 18 × 10^8 = 1.8 × 10^9

Division:

(1.5 × 10^3 ) ÷ (5.0 × 10−2) = 0.3 × 10^5 = 3 × 10^4

(2.1 × 10−2) ÷ (7.0 × 10−3) = 0.3 × 10^1 = 3
(Notice that in division the exponents of 10 are subtracted.)

Addition and subtraction:

(4.2 × 10^4 kg) + (7.9 × 10^3 kg) =

(4.2 × 10^4 kg) + (0.79 × 10^4 kg) (note that the exponents of 10 are now the same)

= 4.99 × 10^4 kg

This can be rounded to 5.0 × 10^4 kg.

(6.02 × 10–3) − (2.41 × 10–4) = (6.02 × 10–3) − (.241 × 10–3) (note that the

exponents of 10 are now the same) = 5.779 × 10–3 or 5.8 × 10–3 when rounded to
two significant figures.

TIP

Cancel out all units except the one for the answer.

Dimensional Analysis (Factor-Label Method of Conversion)

When you are working problems that involve numbers with units of measurement,
it is convenient to use this method so that you do not become confused in the
operations of multiplication or division. For example, if you are changing 0.001
kilogram to milligrams, you set up each conversion as a fraction so that all the
units will factor out except the one you want in the answer.

Notice that the kilogram is made the denominator in the first fraction to be
factored with the original kilogram unit. The numerator is equal to the
denominator except that the numerator is expressed in smaller units. The second
fraction has the gram unit in the denominator to be factored with the gram unit in