1. How to survive WITHOUT your calculator!
Mental Math
How to survive WITHOUT your calculator!

2. Fractions Converting decimals (#’s < 1) to fractions:
Make decimal a fraction
Multiply by numerator
Divide by denominator
Set 1: 0.1 x 0.2
When multiplying 2 fractions:
Multiply the numerators
Multiply the denominators
Simplify
Set 2: 0.1 x 0.6

3. Scientific Notation WITHOUT a Calculator

4. Adding and Subtracting
Step 1: Adjust the powers of 10 in the 2 numbers so that they are the same.
(Tip: It is easier to adjust the smaller power to equal the larger power).
(Tip: One will not be in true scientific notation)
Step 2 : Add or subtract the numbers.
Step 3 : Give the answer in scientific notation.

5. 2.0 x x 103
= .20 x x 103
.2 x x 103
= (.2+3) x 103
= 3.2 x 103
Step 1: Adjust the powers of 10 in the 2 numbers so that they are the same.
(Tip: It is easier to adjust the smaller power to equal the larger power).
(Tip: One will not be in true scientific notation)
Step 2 : Add or subtract the numbers.
Step 3 : Give the answer in scientific notation.
2.0 x x 105
2.0 x x 107
= ( ) x 107
= x 107
1. Make exponents the same
2. Subtract and keep the 107

6. Multiplying To multiply numbers in scientific notation:
Step 1 : Group the numbers together.
Step 2 : Multiply the numbers.
Step 3 : Add the powers of 10.
Step 4 : Give the answer in scientific notation.

7. 3x108 x 1.5x1023 =
(3x1.5)x(108+23)
Step 1 : Group the numbers together.
Step 2 : Multiply the numbers.
Step 3 : Add the powers of 10.
Step 4 : Give the answer in scientific notation.
=4.5x1031
4.0x108 x 5.0x106 =
(4.0x5.0) x =
20x1014
=2.0x1015

8. Dividing To divide numbers in scientific notation:
Step 1 : Group the numbers together.
Step 2 : Divide the numbers.
Step 3 : Subtract the powers of 10.
Step 4 : Give the answer in scientific notation.

9. 4.5x108
3x105
4.5 3
x 108-5
Step 1 : Group the numbers together.
Step 2 : Divide the numbers.
Step 3 : Subtract the powers of 10.
Step 4 : Give the answer in scientific notation.
= 1.5x103

10. Scientific Notation Summary
Adding and subtracting
Make the exponents the same
Multiplying and dividing
Add or subtract the exponents