1. Scientific Notation
A number is expressed in scientific notation when it is written as the product of a number and a power of ten.
The number must be greater than or equal to 1 and less than 10.
7.5 x 10 7
Number greater than or equal to 1, but less than 10
Power of 10 written in exponential form

2. The Distance From the Sun to the Earth
93,000,000

3. Step 1 93,000,000 --> 9.3000000 Move decimal to the left
Leave only ONE number in front of decimal
93,000,000 -->

4. Step 2
Write number without zeros
= 9.3

5. Step 3
Count how many places you moved the decimal
Make that your exponent
93,000,000 = 9.3 x 10 7

6. Practice Problems -----> -----> -----> ----->
Write in scientific notation.
Decide the exponent.
98,500,000 = 9.85 x 10?
64,100,000,000 = 6.41 x 10?
279,000,000 = 2.79 x 10?
420,000= 4.2 x 10?
9.85 x 107
----->
6.41 x 1010
----->
2.79 x 108
----->
----->
4.2 x 105

7. Standard form is the opposite of scientific notation
To write in standard form, move the decimal the same number of places as the exponent.
The sign of the exponent tells which direction to move the decimal. A positive exponent means move the decimal to the right.

8. More Practice Problems
Write in standard form
7.34 x 108
8.7 x 103
9 x 105
Answers
734,000,000
3) 900,000
2) 8,700

9. Let’s get started on the homework
W.S. 3-7 Front AND back
Remember to be quiet!!

10. Warm-Up Write in scientific notation 1.) 2,000,000,000 2.) 36,500,000
3.) 465,000,000,000,000
Write in standard form
4.) 4.62 x 105
5.) 3 x 103

11. What if your number is a decimal?
Step 1:
Move decimal to the right
Leave only one number in front of decimal
>

12. Step 2
Write number without zeros
= 8.96

13. Step 3
Count how many places you moved the decimal
Make that your exponent
Since your number was a decimal to begin with the power is a negative!
= 8.96 x 10 -5

14. Practice Problems -----> -----> -----> ----->
Write in scientific notation.
Decide the power of ten.
= 6.58 x 10?
= 6.41 x 10?
= 1.23 x 10?
= 6.8 x 10?
6.58 x 10-6
----->
6.41 x 10-10
----->
1.23 x 10-8
----->
----->
6.8 x 10-6

15. Standard form is the opposite of scientific notation
To write in standard form, move the decimal the same number of places as the exponent.
The sign of the exponent tells which direction to move the decimal. A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left.

16. More Practice Problems
Write in standard form
4.35 x 10-8
8.7 x 10-6
5.2 x 10-5
Answers 2) 3)