NOTES 3-5 Powers of Ten and Scientific Notation
1) A simpler way to show 2 x 2 x 2 x 2 is to use EXPONENTS.
24 means multiply 2 by itself four times. It is read as “two to the fourth power”.
In 24 _____ is the BASE and _____ is the EXPONENT.
How would we write 10 x 10 x 10 using an exponent? ____________________
2) Complete the table.
Multiply
10
10 x 10
10 x 10 x 10
10 x 10 x 10 x10
10 x 10 x 10 x 10 x 10
Result
# of Zeroes
Result as base
and exponent
3) Study the patterns in the table. Then answer the following questions.
a. How is the number of zeroes related to the number of 10’s that were multiplied
together?
b. How many times would you have to multiply ten by itself to the result 1,000,000?
c. How could you write the multiplication problem in b using and exponent?
d. How could you write 100,000,000,000,000,000,000 using a base of 10 and an
exponent?
4) Remember that when you multiply numbers that end with zeros, multiply the other digits
and then move the place value one place for each zero.
For 2 x 200, find 2 x 2 and then move the decimal 2 places. 400
For 60 x 20 find 6 x 2, then place two zeroes at the end = 1200.
3 x 10,000
3.14159 x 1,000,000
5) Some numbers are too large or too small to be written down easily.
Light travels at the speed of about 186,300 miles per second. Find the distance light travels
in one day.
6) Scientists and mathematicians use their understanding of powers of ten and place value to
write very large and very small numbers in a form that is easier to work with. This form is
called SCIENTIFIC NOTATION.
Multiply 3.2 x 10,000
Write 10,000 as an exponent with a base of ten.
So 3.2 x 10,000 =
=
This final number is written in SCIENTIFIC NOTATION. A number written in scientific
notation is the number written with no place value great than the ONES place, multiplied by a
power of ten.
a) Circle the numbers that are written in scientific notation.
8.8 x 104
52.6 x 103
1 x 10
3.2 x 410
b) Write these numbers in scientific notation.
31,700,000,000
9,600
74,000.44
7) Numbers written without using scientific notation (like the examples above) are written in
what is called STANDARD FORM. You can use your knowledge of powers of ten to
change numbers from scientific notation to standard form. Standard form includes commas
and does NOT include “place finding loops”.
Write the following in standard form:
4.1 x 105
2.894 x 1012
4.99012 x 102