Scientific Notation A short-hand way of writing

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Presentation transcript:

Scientific Notation A short-hand way of writing large and small 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 = 9.3000000

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 sure that you write a 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

93,000,000 --- Standard Form 9.3 x 107 --- 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 3.40000 --- 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

What about a negative exponent? The sign of the exponent tells which direction to move the decimal. A positive exponent means you move the decimal to the right and a negative exponent means you move the decimal to the left.

Negative Exponents in Scientific Notation When you have a negative exponent in scientific notation, you will move the decimal point to the LEFT!! 6.345 * 10¯6 is 0.000006345

What would the following be in standard form….. 3.45 * 10¯4 8 * 10¯8 9.3452 * 10¯7 7.776 * 10¯11 2.209 * 10¯10 0.000345 0.00000008 0.00000093452 0.00000000007776 0.0000000002209

Turn the following into scientific notation… 0.00002352 0.02147 0.0000085 0.00000000009 0.3 0.98888501 0.00000045

What is the Exponent? 2.352 * 10 2.147 * 10 8.5 * 10 9 * 10 3 * 10 9.8888501 * 10 4.5 * 10