1. Scientific Notation

2. Scientific Notation
Represent a number as the product of a coefficient (N) and power of ten (M).
N x 10M
Coefficient: number with only one non- zero digit to the left of the decimal point
4.25 x 103

3. Scientific Notation Number Factored Number # factors of 10
1 x 100 10
1 x 101
100
10 x 10 2
1 x 102
1000
10 x 10 x 10 3
1 x 103
10000
10 x 10 x 10 x 10 4
1 x 104
100000
10 x 10 x 10 x 10 x 10 5
1 x 105
10 x 10 x 10 x 10 x 10 x 10 6
1 x 106

4. # factors of 10 in denominator
Scientific Notation
Number
Factored Number
# factors of 10 in denominator
Scientific Notation 1
1 x 100
0.1
1 10
1 x 10-1
0.01
1 10 x 10 2
1 x 10--2
0.001
1 10𝑥10𝑥10 3
1 x 10-3
0.0001
1 10𝑥10𝑥10𝑥10 4
1 x 10-4
1 10𝑥10𝑥10𝑥10𝑥10 5
1 x 10-5
1 10𝑥10𝑥10𝑥10𝑥10𝑥10 6
1 x 10-6

5. Scientific Notation When writing a number in scientific notation:
A number that is greater than ten (10) will have a positive exponent
A number that is less than one (1) will have a negative exponent

6. Scientific Notation to Standard Form
Positive exponent:
multiply by the number of factors of 10 represented by the exponent.
3.6 x 105 = 3.6 x 10,000 = 360,000
number greater than one

7. Scientific Notation to Standard Form
1.23 x 104 = 6.57 x 102 = x 102 = x 103 =

8. Scientific Notation to Standard Form
Negative exponent:
divide by the number of factors of 10 represented by the exponent
4.7 x 10-3 = 4.7/ 1000 =
number less than one

9. Scientific Notation to Standard Form
1.23 x 10-4 = 6.57 x 10-2 = x 10-5 = x 10-3 =

10. Standard Form to Scientific Notation
Factoring 10’s from a number.
Magnitude (size) of the number must stay the same
Only changing the FORM of the number
100 = 1 x 10 x 10 = 1 x 102
5,250 = 5.25 x 10 x 10 x 10 = 5.25 x 103
= 5.35 / (10,000) = 5.35 x 10-4

11. Standard Form to Scientific Notation
Exponent is the number of places you move the decimal point to obtain the coefficient.
If the number is >10, exponent is positive
If the number is <1, exponent is negative
Coefficient is a number from one to nine

12. Standard Form to Scientific Notation
33,000,000 =
468.9 =
954,000 =
12.5 =

13. Standard Form to Scientific Notation= = = =

14. Scientific Notation on Calculators
Use exponent key (EE or exp)
5 E 5 represents 5 x 105 OR
represents 5 x 105
Record number in proper form, not as it appears on calculator!!!