1. Scientific Notation

2. What is Scientific Notation?
Scientific notation is a way of writing numbers
It is very convenient to express numbers that are too large or too small to be written in decimal form in a simpler way
Try multiplying 1,234,000,000,000 by ; is there an easy way to write the result?
Scientific notation allows us to write and handle numbers in a concise manner
Why would it be beneficial to write numbers in scientific notation?
When do you use very large or very small numbers anyway?

3. Two Parts to Scientific Notation
Numbers written in scientific notation look like to following:
N x 10X
Read it as “N times TEN to the power of X”
Notice that there are two main components:
N, which is called the “Mantissa”
N can be any number
X, which is called the “Exponent”
X MUST be an integer

4. Pop Quiz N x 10X No Yes 4.8756 x 1000 .01867x109 Yes No 2.37895 x 102
Are the following numbers written in scientific notation? No
Yes
x 1000
.01867x109
Yes No
x 102
22.479x10-4
239 x 1004
9.74 x 104,660

5. Converting Standard Form to Scientific Notation
N x 10X
Put the decimal point after the first, second, or third digit.
The leftmost digit should always be between 1-9; it CANNOT be a ZERO
Count the number of places that the decimal point was moved from its original location. This number will be your exponent
If the new position of the decimal point is to the left of its original, the exponent is treated as positive
If the new position of the decimal point is to the right of its original, the exponent is negative

6. Examples
N x 10X
Converting standard form to scientific notation
248 = 2.48x102
= 5.47x10-5
= x10-2
4,378,000,000 = 4.378x109
314,150,000,000,000 = x1013

7. Converting Scientific Notation to Standard Form
N x 10X
Notice two things:
The location of the decimal point in the mantissa
The sign of the exponent
If the sign of the exponent is positive, move the decimal point in the mantissa X digits to the right
If the sign of the exponent is negative, move the decimal point in the mantissa X digits to the left
Fill in any empty spaces between the last number in the mantissa and the new position of the decimal point with ZEROS

8. Examples
N x 10X
Converting scientific notation to standard form
3.086x106 = 3,086,000
547x10-4 = .0547
5.8756x102 =
x1010 = 439,950,050,000
.5x101 = 5