Scientific Notation

Scientific Notation Why do we need to know this?

◦ It’s hard to work with numbers like this: ◦ 6,000,000,000,000,000,000,000◦ Or this 0.00000000000000000000876

What is scientific notation?◦ Simplifying large or small numbers by converting them to

a number between 1 and 10 multiplied by powers of 10

Scientific Notation Powers of 10?

◦ 10 x 10 x 10 = 1000 or 103

◦ 10-n = 1/10n ◦ So 10-3 = 1/103 = 1/1000 = 0.001

Converting Standard notation to Scientific Notation

Always move the decimal so there is one number LEFT of the decimal◦ If the original number is LARGER than 1 and the decimal

is moved to the LEFT, use a positive exponent◦ 1,567 = 1.567 x 103

◦ If the original number is SMALLER than 1 and the decimal is moved to the RIGHT, use a negative exponent◦ 0.0000045 = 4.5 x 10-6

1. Move the decimal to the right of the first non-zero

number.2. Count how many places the

decimal had to be moved.3. If the decimal had to be moved

to the right, the exponent is negative.

4. If the decimal had to be moved to the left, the exponent is positive.

To write a number in scientific notation:

Converting from scientific notation to Standard notation

Move the decimal the number of places indicated by the exponent.◦ If the exponent is positive, your final number should be

larger than 15.6 x 102 = 560

◦ I f the exponent is negative, your final number should be smaller than 1◦ 5.6 x 10-2 = 0.056

MultiplicationWhen multiplying numbers written in scientific notation…..multiply the first factors and add the exponents.

Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105)

Solution: Multiply 3.2 x 2.1. Add the exponents -3 + 5

Answer: 6.7 x 102

DivisionDivide the numerator by the denominator. Subtract the exponent in the denominator from the exponent in the numerator.

Sample Problem: Divide (6.4 x 106) by (1.7 x 102)

Solution: Divide 6.4 by 1.7. Subtract the exponents 6 - 2

Answer: 3.8 x 104

Adding and Subtracting inScientific Notation

(5.8 x 103) + (2.16 x 104)

Step 1 – move the decimal of one so they both have the same power of ten

(5.8 x 103) + (21.6 x 103)

Step 2 – add or subtract the numbers without their powers of ten exponents

5.8 21.6 = 27.4

Step 3 – rewrite with the same power of ten.

27.4 x 103

Step 4 – move the decimal (if needed) to get it back into scientific notation form

2.74 x 104