Powers of Ten Review

Powers of 10 indicate how many time to multiply 10 by itself. For example,

103 = 10 10 10 = 1, 000106 = 10 10 10 10 10 10 = 1, 000, 000

Negative powers are the reciprocals of the corresponding positive powers. For example,

103 =1

103=

1

1, 000= 0.001

106 =1

106=

1

1, 000, 000= 0.000001

A positive exponent tells how many zeros follow the 1. For example

100 = 1

101 = 10

102 = 100

103 = 1, 000 a thousand106 = 1, 000 a million109 = 1, 000 a billion1012 = 1, 000 a trillion

A negative exponent tells how many places are to the right of the decimal point, including the 1.

For example.

100 = 1

101 = 0.1

102 = 0.01

103 = 0.001 a thousandth106 = 0.001 a millionth109 = 0.001 a billionth1012 = 0.001 a trillionth

The three most important properties we will use are multiplication, division, and powers

10a 10b = 10a+b10a 10b = 10ab

(10a)b = 10ab

As implied above we will use the Short Scale for the names of large and small numbers in

this course: Every new term greater than million is one thousand times larger than the previous

term. Thus, billion means a thousand millions (109), trillion means a thousand billions (1012), and

so on.