6th Grade Math Textbook, Fundamentals

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4-9

0.001 one thousandth

Think

10 ^2  0.01

The negative exponent indicates that the

decimal is between 0 and 1.

The number 2 indicates that the decimal

will have 2 decimal places.

1

100

1

102

Remember:Any nonzero number

with zero as an exponent equals 1.

a^0 1, a 0

Negative exponents are used

to express decimals that have

values between 0 and 1.

Update your skills. See page 407 I.

Negative Exponents

Objective To express powers with negative exponents as decimals •To express decimals as

powers with negative exponents • To simplify expressions with negative exponents

In science class, Gloria measures the length of a microorganism
as 0.001 millimeter. She knows that this length is less than
1 millimeter and greater than 0 millimeters. How can she write
this number as a power of 10?

To write 0.001 as a power of 10, rewrite the decimal as a

fraction. Apply the Law of Exponents for Division to write

a decimal as a power of 10.

0.001  Write the decimal in fraction form.



 100 ^3 Apply the Law of Exponents for Division.

 10 ^3

So the microorganism’s length of 0.001 millimeter is 10^3 mm.

The pattern in a place-value chart can also help you use

negative exponents to express any decimal that is a power of 10.

Write 0.00001 as a power of 10 in exponent form.

Notice that the number in each negative exponent is the same as the

number of decimal places to the right of the decimal point. Using this

pattern, you can see that 0.00001 can be expressed as 10^5.

You can write a decimal for a power

of 10 given in exponent form.

Write 10^2 as a decimal.

10 ^2 0.01

You can evaluate a power that has

any nonzero integer as the base

and a negativeexponent.

100

103

Thousands

103

Hundreds

102

Tens

101

Ones

100

Tenths

10 ^1

Hundredths

10 ^2

Thousandths

10 ^3

1000 100 10 1 0.1 0.01 0.001

1

1000

Write the numerator and the denominator as

powers of 10: 1000 10 • 10 • 10  103.

Key Concept

Negative Exponents

Any nonzero number to the negative npower can be

written as 1 divided by the number to the nth power.

For any integer nand any number a, a 0,ana^1 n.