# 4.1 Integer Powers of Ten - P by cuiliqing

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4.1 Integer Powers of Ten
You will evaluate powers with positive
numbers, negative numbers, or zero for
exponents.

Essential Question: How do you evaluate a
power of ten with a negative exponent?
Daily Warm-Up Exercises    For use with pages 195–200

Evaluate.

Order the numbers from least to greatest.

3. –5, 2, –7, 1, 10       ANSWER      –7, –5, 1, 2, 10

4. 12, 14, –19, 22, –24   ANSWER      –24, –19, 12, 14, 22
Activities

   Secret Worlds: The Universe Within

   Zero and Negative Powers of Ten
   Textbook p. 195
Definitions

   100 = 1
   a0 = 1         any number to the power
of zero equals 1

   10-n =    1   10-n is the reciprocal of 10n
10n

   a-n =     1    a-n is the reciprocal of an
an
To Convert Decimals (Standard Form)
to Powers of Ten:
   If the number is bigger than 1:
   The power will equal the number of zeros

   If the number is less than 1, but bigger than 0:
   Make the number into a fraction
   The power will equal the opposite (negative) of the number
of zeros in the denominator

   If the number is 1:
   The power is 0
Example 1         Write Powers of 10 in Standard Form

a. 10 3 = 10  10  10 = 1,000

1   1   1   1   1
b.   10 –5   =                = 0.00001
10 10 10 10 10
Guided Practice   for Example 1

Write the power of 10 in standard form.

Guided Practice    for Example 1

5. SCIENCE
Scientists have created a microfabric using molded
plastic. Its narrowest threads are 10 –3 millimeter across.
Write this number in standard form.

Example 2      Write Numbers in Standard Form as Powers of 10

There are 9 zeros after the 1 so the
a. 1,000,000,000 = 10 9     exponent is 9.

There are 5 = 6 – 1 zeros after the
b. 0.000001 = 10 –6         decimal point, so the exponent
is – 6.
Example 3     Using a Negative Exponent

STROBE LIGHTS
The picture of the golf ball was taken using a strobe
light. Each flash of the strobe light lasts about
1 microsecond. Use a power of 10 to write this time in
seconds.

SOLUTION
Each flash lasts 1 microsecond, or equivalently,
1     second.
1,000,000
1       1
= 6             Write 1,000,000 as 106.
1,000,000  10
Example 3      Using a Negative Exponent

1
= 10 –6        Use the fact that        = 10 –n.
10 n

Each flash of the strobe light lasts about 10 –6 second.
Guided Practice    for Examples 2 and 3

6. Write the number 0.0001 as a power of 10.

7. WHAT IF?
In Example 3, suppose each flash of the strobe
light lasts one millisecond (or one thousandth of
a second). Use a power of 10 to write this time in
seconds.

Example 4         Multiple Choice Practice

Which list of numbers is ordered from least to greatest?

10 2, 10 –3, 0.0001, 1, 10        10 –3, 0.0001, 1, 10, 10 2

0.0001, 10 –3, 1, 10, 10 2        0.0001, 1, 10, 10 2, 10 –3

SOLUTION
Write each number in standard form. Then compare the
numbers.
10 2 = 100, 10 –3 = 0.001, 0.0001, 1, 10
Example 4      Multiple Choice Practice

The order of the numbers from least to greatest is
0.0001, 10 –3, 1, 10, and 10 2.

Guided Practice         for Example 4

Order the numbers from least to greatest.

8. 100, 10 –2, 1                  ANSWER    10 –2, 1, 100

9. 0.01, 10 2, 1                  ANSWER    0.01, 1, 10 2

10. 10, 10 0, 10 –1, 10 2         ANSWER    10 –1, 10 0, 10, 10 2
Essential Question:

How do you evaluate a power of ten
with a negative exponent?
Independent Practice

   Textbook p. 198-200 (1-15, 19, 23, 29-31, 39-
41)

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