SKILL: USING EXPONENTS
EM Frequencies
MATH TUTORIAL
CLASSZONE.COM
Click on Math Tutorial for
more help with positive and
negative exponents.
The Chandra X-Ray Observatory in the photograph is a space
telescope that detects high-frequency EM waves called x-rays. A
wave’s frequency is the number of peaks that pass a given point in
1 second. EM frequencies usually run from about 100 Hz to about
1 trillion trillion Hz. If written in standard form (using zeros), 1 trillion
trillion would look like this:
1,000,000,000,000,000,000,000,000
Because this number is hard to read, it would be helpful to write
it more simply. Using exponents, 1 trillion trillion can be written
as 1024.
Exponents can also be used to simplify very small numbers. For
example, the wavelength of a wave with a frequency of 1024 Hz is
about one ten-thousandth of one trillionth of a meter. That number
can be written in standard form as 0.000,000,000,000,000,1 m.
Using exponents, the number can be written more simply as 10–16 m.
Examples
Large Numbers
To write a multiple of 10 in exponent form, just count the zeros.
Then, use the total as the exponent.
(1) 10,000 has 4 zeros.
(2) 4 is the exponent.
ANSWER 104 is the way to write 10,000 using exponents.
Decimals
To convert a decimal into exponent form, count the number of
places to the right of the decimal point. Then, use the total with
a negative sign as the exponent.
(1) 0.000,001 has 6 places to the right of the decimal point.
(2) Add a negative sign to make the exponent –6.
ANSWER 10–6 is the way to write 0.000,001 using exponents.
Answer the following questions.
The top photograph shows a visible-light
image of the Crab Nebula. The bottom
photograph shows the same nebula as
it appears at higher x-ray frequencies.
510 Unit 4: Waves, Sound, and Light
Write each number using an exponent.
1. 10,000,000
3. 100,000
2. 0.000,01
4. 0.0001
Write the number in standard form.
7. 108
9. 1011
–8
8. 10
10. 10–12
5. 10,000,000,000
6. 0.000,000,001
11. 1017
12. 10–15
CHALLENGE Using exponents, multiply 102 by 103. Explain
how you got your result.