SCIENTIFIC NOTATION Scientific Notation In science we typically

SCIENTIFIC NOTATION

Scientific Notation • In science, we typically see very LARGE or very small numbers in our calculations. • Scientific notation is used to reduce the errors when counting ZEROES.

Scientific Notation • In order to make this easier, scientists express numbers in scientific notation, which uses powers of 10.

Scientific Notation • In scientific notation, numbers are written in the form: M x 10 n Where the factor M is a number greater than or equal to 1 but less than 10 and n is a whole number.

If you have a BIG number… • You will use POSITIVE powers • For Example: 100000 • 1 x 1010 = 100000 • 1 x 105 =

If you have SMALL numbers… • You will use NEGATIVE powers • For example: • 1 x 10 -5 = 0. 00001 • 1 x 10 -10 = 0. 000001

Rules 1. Move the decimals over so that only one nonzero is to the left of the decimal. 5, 500, 000 5. 50000 0. 000067 00006. 7

Rules 2. Count how many spaces you moved the decimal. • If you move to the left it’s positive. If you move to the right it’s negative. 5. 50000 moved 9 spaces left (+9) 00006. 7 moved 9 spaces right (-9)

Rules 3. Get rid of any numbers that are not significant. 5. 50000 5. 5 00006. 7

Rules 4. Write down the number, multiplied by 10 to the power of however many spaces you found in step 2. 5, 500, 000 5. 5 x 109 0. 000067 6. 7 x 10 -9

Practice 1. 457800000 2. 260700 3. 2200 4. 0. 034 5. 0. 000678 6. 0. 0000056 4. 578 x 108 2. 607 x 105 3 2. 2 x 10 3. 4 x 10 -2 -4 6. 78 x 10 5. 6 x 10 -6

Scientific Notation -> Standard Form 1. 5. 89 x 10 -2 2. 4. 932 x 10 -1 3. 9. 7 x 10 -6 4. 6. 01 x 107 5. 2. 485 x 105 6. 1. 45 x 103 0. 0589 0. 4932 0. 0000097 60100000 248500 1450