Algebra 1 Common Core Student Edition, Grade 8-9

You can use the property for multiplying powers with the same base to multiply two

numbers written in scientific notation.

How do you find
t he num ber of
m olecules?
Use u n i t an al ysi s. Di vi d e
out the common units.

Pro b lem 3 Multiplying With Scientific Notation ^ 22)

Ch em i st r y At 20°C, one cubic meter of water has a mass

of about 9.98 x 10 5 g. Each gram of water contains

about 3.34 x 10 22 molecules of water. About how

many molecules of water does the droplet of

water shown below contain?

molecules of water = cubientetCTs cubie-iSTeters grams grams molecules Use uni t an al ysi s.

= (1.13 X 10 7) • (9.98X 10s) • (3.34X 1022) Su b st i t u t e.

Co m m u t at i ve an d

= (1.13 • 9.98 • 3.34) X (l0~7 • 10s • 1022)

37.7 X 10-^74 .54-22

= 37.7 X 10 ,20

= 3.77 X 1021

The droplet contains about 3.77 X 1021 molecules of water.

associat ive properties

of multiplication

Multiply. Add exponents.

Si m p l i f y.

Write in scientific notation.

Go t It? 3. About how many molecules of water are in a swimming pool that holds

200 m 3 of water? Write your answer in scientific notation.

Recall that you can use powers of 10 to make writing very large and very small numbers

more convenient. In scientific notation, you can write any number as a X 10b, where

1 < \a\ < 10. For example, 256,000 is written in scientific notation as 2.56 X 105.

Exponents can also be expressed as fractions. Fractional exponents are called rational

exponents.

Recall that 32 means 3 • 3, which equals 9. You can write the same expression using

rational exponents: 9^. The equation 9 2 = b indicates that b is the positive number that

when multiplied by itself, equals 9.

9^ = 3 since 3*3 = 9.

In general, ak=b means that b multiplied as a factor m times equals a.

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Lesso n 7-2 Multiplying Powers With the Same Base^427