1. Scientific Notation
Mrs Vass
BJH

2. Scientific Notation which is 6.7 x 1010
Definition: Scientific notation is a symbol that expresses any number as a power of ten multiplied by a number between 1 and 10 (including 1).
Scientific notation allows you to work with very large numbers and very small numbers.
A number like would be x 10 9
5 > 1 and < 10 and there are 9 places past where the new decimal place would be.
Write the scientific notation for
which is x 1010

3. Scientific Notation
Which of the following numbers are in scientific notation? If it is not, explain why. 
a.    3 x 106 
b.   4.6 x 10-4 
c.    0.2 x 108
d.   2.8 x 100
Answers
A) is correct scientific notation as the decimal number is less than 10 and equal to or greater than 1. It is also written in a power of 10
B) is correct for the same reasons as A
C) is not correct as the decimal number is less than 1
D) is not correct as the decimal is correct but it is not written in a power of 10 . If it was changed to it would be correct

4. Scientific Notation
How do we represent very small numbers in scientific notation?
Recall that = 5 x or x 1
Therefore, armed with the above knowledge, our previous knowledge of negative exponents, and the
definition for scientific notation, is represented in scientific notation as x

5. Scientific Notation The calculator only holds 7 digits.
So if you have a number like it would show it as 7.62 x
If you have a positive exponent for 10, then the decimal place will move to the right and make the number bigger such as
3.45 x 105 =
If you have a negative exponent , the decimal point will move to the left and make the number smaller such as x 10 –5 =

6. Scientific Notation Trivia
106 million
billion
trillion
quadrillion
quintillion
sextillion
googol

7. Scientific Notation Trivia
The word googol was created in 1938 by the 11 year old nephew of the American mathematician Edward Kasner.

8. Operations with Scientific Notation
Numbers can be written in standard form ( as a number) and scientific notation.
You can do operations such as add, subtract , multiply and divide with scientific notation.
Scientific notation allows you to solve more easily with very large or very small numbers.
Remember that scientific notation is written in POWERS OF 10

9. Adding numbers with scientific notation:
1.4 x x 10-3
If the power of 10 is the same then you can take out the power of 10 and then ADD the other two factors.
For example:
( ) x 10-3
3.7 x written in standard form it
would be

10. Addition with Scientific Notation
If the numbers are not in the same power of 10, then you might be able to rewrite the numbers so that they are in the same power of 10.
5.3 x x could be rewritten as
0.53 x x 10 5
( Now you can solve it as shown in previous slide)
( ) x 10 5
6.73 x written in standard form is

11. Subtraction with Scientific Notation
Subtraction is done the same way as addition. Take out the power of 10 and then subtract the other factors.
7.3 x x 10 3
( 7.3 – 6.2) x 10 3
1.1 x 10 3
written in standard form it is

12. Multiplying in Scientific Notation
When you multiply or divide with scientific notation , you will use your exponent laws. Remember , when we multiply powers with the same base , we add the exponents:
(2.2 x 104 ) x ( 1.2 x 10 7)
Remember that the Commutative Property
allows us to rearrange the FACTORS without affecting the answer.
SO : x 1.2 x 104 x 10 7
2.64 x 10 (4 + 7)
x or

13. Dividing with Scientific Notation
12.4 x ÷ 3.2 x 10 6
and
x 10 (10 – 6)
= x OR
You need to divide the first factors and then apply the exponent laws to the powers of 10.