1. Writing Numbers That Are Too Big or Too Small in Decimal Form
SCIENTIFIC NOTATION
Writing Numbers That Are
Too Big or Too Small
in Decimal Form

2. Definitions Scientific Notation Power of Ten Negative Exponent
A number between one and ten, including one, multiplied by a power of ten.
Power of Ten
A product of multiplying ten by itself one or more times.
Negative Exponent
The opposite of a power of a number; used to express smaller numbers.

3. Standard Notation to Scientific Notation
137,000,000
can be rewritten as
Scientific Notation:
1.37× 10 8

4. Steps Write 312,000,000,000 in Scientific Notation. Step One
Move the decimal place to the left to create a new number from 1 up to 9.
Where is the decimal point in 312,000,000,000?
Because this is a whole number, the decimal point is understood to be at the end of the number: 312,000,000,000
Decimal Point

5. Steps 312,000,000,000 becomes Step Two Step Three 3 12 Drop all zeros
3 12
Step Two
Drop all zeros
Step Three
Count the number of places from the old decimal point to the new decimal point.
In this case, there are 11 places.

6. Steps
312,000,000,000
3 12
Step Four
Multiply by power of 10 and add the exponent:
3 12 x

7. Practice Rewrite the Standard Notation numbers as Scientific Notation:
347,000
3.47× 10 5
902,000,000
9.02× 10 8
61,400
6.14× 10 4

8. Scientific Notation to Standard Notation
The process is reversed in two steps!
1.23× 10 5
Step One
Look at the exponent:
Step Two
Move the decimal point five places to the right!
123,000

9. Practice Rewrite the Scientific Notation numbers as Standard Notation:
6.806× 10 6
4× 10 3
2× 10 6
3.104× 10 11
6,806,000
4,000
2,000,000
310,400,000,000

10. Mixed Review
32,300
2.612× 10 6
16.12
3.06× 10 4
6.1028× 10 10
3.23× 10 4
2,612,000
1.612× 10 1
30,600
61,028,000,000

11. Practice
In the United States, 15,000,000 households use private wells for their water supply.
Write this number in scientific notation.
1.5× 10 7

12. Practice
The U.S. has a total of 𝟏.𝟐𝟗𝟏𝟔× 𝟏𝟎 𝟕 acres of land reserved for state parks.
Write this in standard form.
12,916,000 acres

13. Negative Exponents 1000 = 10 x 10 x 10 = 103 100 = 10 x 10 = 102
10 = 101
1 = 100
Do you see a pattern?
Can you guess what the next exponent will be?

14. Negative Exponents 1 = = = =
10-4

15. Practice Rewrite the following decimals with negative exponents.
8.2 X 10-4
5.9 X 10-7
4 X 10-5

16. Practice
1.248× 10 −6
6.123 × 10 −5
𝟑.𝟎𝟔× 𝟏𝟎 −𝟔
𝟖.𝟗𝟐 × 𝟏𝟎 −𝟒

17. Practice
The nucleus of a human cell is about 7× 10 −6 meters in diameter.
Write this number in standard notation.

18. Practice
A ribosome, another part of a cell, is about of a meter in diameter.
Write the length in scientific notation.
𝟑× 𝟏𝟎 −𝟗