# Scientific Notation A short-hand way of writing large numbers without

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Scientific Notation A short-hand way of writing large numbers without
writing all of the zeros.

The Distance From the Sun to the Earth
93,000,000

Step 1 93,000,000 = 9.3000000 Move decimal left
Leave only one number in front of decimal 93,000,000 =

Step 2 Write number without zeros 93,000,000 = 9.3

Step 3 7 93,000,000 = 9.3 x 10 Count how many places you moved decimal
Make that your power of ten 93,000,000 = 9.3 x 10 7

The power of ten is 7 because the decimal moved 7 places. 7
93,000,000 = 9.3 x 10 7

93,000, Standard Form 9.3 x Scientific Notation

Practice Problem -----> -----> -----> ----->
Write in scientific notation. Decide the power of ten. 98,500,000 = 9.85 x 10? 64,100,000,000 = 6.41 x 10? 279,000,000 = 2.79 x 10? 4,200,000 = 4.2 x 10? 9.85 x 107 -----> 6.41 x 1010 -----> 2.79 x 108 -----> -----> 4.2 x 106

More Practice Problems
On these, decide where the decimal will be moved. 734,000,000 = ______ x 108 870,000,000,000 = ______x 1011 90,000,000,000 = _____ x 1010 Answers 3) 9 x 1010 7.34 x 108 2) 8.7 x 1011

Complete Practice Problems
Write in scientific notation. 50,000 7,200,000 802,000,000,000 Answers 1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011

Scientific Notation to Standard Form
Move the decimal to the right 3.4 x 105 in scientific notation move the decimal ---> 340,000 in standard form

Move the decimal to the right.
Write in Standard Form Move the decimal to the right. 6.27 x 106 9.01 x 104 6,270,000 90,100

Positive Exponents 101 = 10 102 = 10X10= 100 103 = 10X10X10 = 1000

Negative Exponents 10-1 = 1/10 = 0.1 10-2 = 1/100 = 0.01
10-3 = 1/1000 = 0.001 10-4 = 1/10000 =

Scientific Notation We use the idea of exponents to make it easier to work with large and small numbers. 10,000 = 1 X 104 250,000 = 2.5 X 105 Count places to the left until there is one number to the left of the decimal point. 230,000 = ? 35,000 = ?

Scientific Notation Continued
= 6 X 10-5 = 4.5 X 10-4 Count places to the right until there is one number to the left of the decimal point 0.003 = ? = ?

Multiplying with Scientific Notation
Add the Exponents 102 X 103 = 105 100 X 1000 = 100,000

Multiplying with Scientific Notation
(2.3 X 102)(3.3 X 103) 230 X 3300 Multiply the Coefficients 2.3 X 3.3 = 7.59 Add the Exponents 102 X 103 = 105 7.59 X 105 759,000

Multiplying with Scientific Notation
(4.6 X 104) X (5.5 X 103) = ? (3.1 X 103) X (4.2 X 105) = ?

Dividing with Scientific Notation
Subtract the Exponents 104/103 = 101 10000X 1000 = 10

Dividing with Scientific Notation
(3.3 X 104)/ (2.3 X 102) 33000 / 230 = Divide the Coefficients 3.3/ 2.3 = Subtract the Exponents 104 / 102 = 102 X 102

Dividing with Scientific Notation
(4.6 X 104) / (5.5 X 103) = ? (3.1 X 103) / (4.2 X 105) = ?