Scientific Notation
Infinity Mirrored Room — The Souls of Millions of Light Years Away Yayoi Kusama, 2013
How wide is our universe?
210,000,000,000,000,000,000,000 miles
(22 zeros)
This number is written in expanded form. When numbers get this large, it is easier to write them in scientific notation.
Scientific Notation
A number is expressed in scientific notation when it is in the form
a x 10n
where a is between 1 and 10 and n is an integer
Write the width of the universe in scientific notation.
210,000,000,000,000,000,000,000 miles
Where is the decimal point now?
After the last zero.
Where would you put the decimal to make this number be between 1 and 10?
Between the 2 and the 1
2.10,000,000,000,000,000,000,000.
How many decimal places did you move the decimal?
23
When the original number is greater than 1, the exponent is positive.
The answer in scientific notation is
2.1 x 1023
1) Express 0.0000000902 in scientific notation.
Where would the decimal go to make the number be between 1 and 10?
9.02
The decimal was moved how many places?
8
When the original number is less than 1, the exponent is negative.
9.02 x 10-8
Write 28750.9 in scientific notation.
2) Express 1.8 x 10-4 in decimal notation.
0.00018
3) Express 4.58 x 106 in decimal notation.
4,580,000
On the graphing calculator, scientific notation is done with the button.
4.58 x 106 is typed 4.58 6
4) Use a calculator to evaluate: � 4.5 x 10-5� 1.6 x 10-2
= 0.0028125
Answer in scientific notation. Rounded for sig figs
2.8125 x 10-3 2.8 x 10-3
5) Use a calculator to evaluate: � 7.2 x 10-9� 1.2 x 102
On the calculator, the answer is:
6E-11
The answer in scientific notation is
6 x 10-11 (6.0 x 10-11 w/ sig figs)
The answer in decimal notation is
0.000000000060
6) Use a calculator to evaluate �(3,600,000,000)(23)
On the calculator, the answer is:
8.28E +10
The answer in scientific notation is
8.3 x 1010 w/ sig figs
The answer in decimal notation is
83,000,000,000