Name:
Date:
Period:
Scientific Notation Notes
Scientific notation is simply a method for expressing and working with very large or very
small numbers in a ____________________. It is also used to indicate the relative
degree of ____________ of a measurement or value.
The formula for scientific notation is ____________, where:
a = A rational number having _______ non-zero digit to the left of the decimal point
and _____________________ to the right of the decimal point.
b = Any rational whole number exponent.
Steps to convert a number to scientific notation:
1. To convert a number into scientific notation, you should move the decimal point
until only one nonzero digit is to the left of the decimal point to get your value for __.
2. The value for __ will be the number of places you have moved the decimal point. If
you move the decimal to the left, the exponent will be positive (you will be
multiplying by 10 to reach the original number), and if you moved the decimal to the
right, the exponent will be negative (you will be multiplying by .1 to reach the
original number).
3. Plug in your values for a and b into your scientific notation formula.
Example:
Convert 35,356 into Scientific Notation
1. Move the decimal point until you have one digit to the left of the decimal (a =
3.5356).
2. Because you moved the decimal four points to the left, your value for n will be 4,
b = 4.
3. Plug your values into the scientific notation formula. 3.5356 x 104 = 35,356.
Notes about exponents:
Any number to the ___ power = ___, so if you do not move the decimal at all, then your
value for b would be 0. Example: 3.2 in scientific notation would be 3.2 x 100.
Extra Notes:
Steps to add and subtract values in scientific notation:
1. The numbers being added or subtracted must have the same value for b. If the
values are different, you must convert the numbers so that the values for n are the
___________.
2. Add and subtract you’re a values __________ and write down your solution.
3. You value for ___ will state the same.
4. Plug you new values for a and b into the scientific notation __________.
5. Make sure your new answer is in correct scientific notation (a should have only one
digit to the left of the decimal). If you answer is not in correct scientific notation,
please use the steps above to convert to scientific notation.
Example:
(4 x 102) + (3 x 103) =
1. (4 x 102) + (30 x 102)
2. 4 + 30 = a, a = 34
3. b = 2
4. 34 x 102
5. Solution is 3.4 x 103
(4 x 102) – (2 x 103) =
1. (4 x 102) + (30 x 102)
2. 4 - 20 = a, a = -16
3. b = 2
4. -16 x 102
5. Solution is -1.6 x 103
Steps to multiply and divide values in scientific notation:
1. Multiply or divide your a values normally and write down your new ___.
2. _____ (multiplication) or ____________ (division) your b values to one another and
write the new exponent value.
3. Plug your new values for a and b into the scientific notation formula.
4. Make sure your new answer is in correct scientific notation (a should have only one
digit to the left of the decimal). If you answer is not in correct scientific notation,
please use the steps to convert to scientific notation.
Example:
(4 x 102) (3 x 103) =
1. 4 x 3 = a, a = 12
2. 2 + 3 = b, b = 5
3. 12 x 105
4. Solution is 1.2 x 106
Extra Notes:
(4 x 102) / (2 x 103) =
1. 4 / 2 = a, a = 2
2. 2 - 3 = b, b = -1
3. 2 x 10-1
5. Solution is 2 x 10-1
Name:
Date:
Period:
Scientific Notation Sample Problems
Express the following in scientific notation:
1. 500
a=
b=
Solution =
2. 0.6
a=
b=
Solution =
3. 3,447
a=
b=
Solution =
4. 23,000
a=
b=
Solution =
5. .00008
a=
b=
Solution =
6. 35
a=
b=
Solution =
7. 200,000
a=
b=
Solution =
Add:
9. (3 x 10-1) + (6 x 10-2)
a=
b=
Solution =
Multiply:
11. (5.08 x 10-1) (8.07 x 105)
a=
b=
Solution =
8. 725
a=
b=
Solution =
Subtract:
10. (3 x 10-1) - (6 x 10-2)
a=
b=
Solution =
Divide:
12. (5.08 x 10-1) / (8.07 x 105)
a=
b=
Solution =
13. (3.57 x 103) (2.45 x 104)
a=
b=
Solution =
14. (3.57 x 103) / (2.45 x 104)
a=
b=
Solution =
Compute:
15. [(4 x 10-7) + (3 x 103)] / (1.879 x 100) + (3.2 x 106)
16. [(7.22 x 102) - (2.05 x 103)] / [(5.32 x 103) + (3.42 x 104)]