Chapter 4-8 Scientific Notation UNIT 2 Chapter 4-8 Scientific Notation

Scientific Notation When you deal with very large numbers like 5,000,000 or very small numbers like .00005, it is difficult to keep track of the place value. We can use Scientific Notation as a shorthand way of writing number using powers of 10. A number expressed in scientific notation is written as the product of a factor and a power of 10 That factor must be greater or equal to 1 and less than 10.

Scientific Notation Example: The number 5,000,000 written in Scientific Notation would look like: 5,000,000 = 5.0 x 10 6 Factor is 5 (greater than 1, less than 10) .0004 = 4 x 10 −4 Factor is 4 (greater than 1, less than 1)

Express the number in Scientific Notation 60,000,000 = 6.0 x 10,000,000 {the decimal moves 7 places to the left. **If the decimal moves to the left, the exponent is positive} = 6.0 x 10 7 .000039 = 3.9 X .00001 {The decimal moves 5 places to the right. **If the decimal moves to the right, the exponent is negative} = 3.9 x 10 −5

Standard Notation Standard Notation is simplifying the product of 2 factors If the exponent is positive – move the decimal to the right If the exponent is negative – move the decimal to the left **The decimal will tell you how many times to move right or left

Express the number in Standard Notation 3.76 x 10 5 = 3.76 = 37,600 {move your decimal 5 places to the right and fill in empty spaces with zeroes} 5.1 x 10 −3 = 5.1 = .0051 {move your decimal 3 place to the left and fill in empty spaces with zeroes} 7 x 10 2 = 7. = 700 {move your decimal 2 places to the right and fill empty spaces with zeroes}

Let’s Try Some Examples! Express each number in scientific notation 3,200 2)70,000 3)800,000 Express each number in standard form 4) 4.35 x 10 4 5) 6.49 x 10 −6

Let’s Check Our Answers! Express each number in scientific notation 3,200 2)70,000 3)800,000 3.2 x 10 3 7 x 10 4 8 x 10 5 Express each number in standard form 4) 4.35 x 10 4 5) 6.49 x 10 −6 43,500 .00000649