scientific notation

scientific notation

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scientific notation

Sometimes, especially when you are using a calculator, you 
may come up with a very long number. It might be a big number, 
like 2,890,000,000. Or it might be a small number, like 
0.0000073.
 
Scientific notation is a way to make these numbers easier to 
work with. In scientific notation, you move the decimal place 
until you have a number between 1 and 10. Then you add a power 
of ten that tells how many places you moved the decimal.

In scientific notation, 2,880,000,000 becomes 2.88 x 109. How? 

1. Remember that any whole number can be written with a decimal 
point. For example: 2,890,000,000 = 2,890,000,000.0
2. Now, move the decimal place until you have a number between 1 
and 10. If you keep moving the decimal point to the left in 
2,890,000,000 you will get 2.89.
3. Next, count how many places you moved the decimal point. You 
had to move it 9 places to the left to change 2,890,000,000 to 
2.89. You can show that you moved it 9 places to the left by noting 
that the number should be multiplied by 109.
2.89 x 109 = 2.89 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10
2.89 x 109 = 2,890,000,000 

Scientific notation can be used to turn 0.0000073 into 7.3 x 10-6.

1. First, move the decimal place until you have a number between 1 
and 10. If you keep moving the decimal point to the right in 
0.0000073 you will get 7.3.
2. Next, count how many places you moved the decimal point. You 
had to move it 6 places to the right to change 0.0000073 to 7.3. 
You can show that you moved it 6 places to the right by noting 
that the number should be multiplied by 10-6.

7.3 x 10-6 = 0.0000073

Remember: in a power of ten, the exponent--the small number 
above and to the right of the 10--tells which way you moved the 
decimal point.

A power of ten with a positive exponent, such as 105, 
means the decimal was moved to the left.
A power of ten with a negative exponent, such as 10-5, 
means the decimal was moved to the right.

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Powers of Ten 
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billions
109 = 1,000,000,000
10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000,000 
millions
106 = 1,000,000
10 x 10 x 10 x 10 x 10 x 10 = 1,000,000 
hundred thousands
105 = 100,000
10 x 10 x 10 x 10 x 10 = 100,000 
ten thousands
104 = 10,000
10 x 10 x 10 x 10 = 10,000 
thousands
103 = 1,000
10 x 10 x 10 = 1,000 
hundreds
102 = 100
10 x 10 = 100 
tens
101 = 10 
ones
100 = 1 
tenths
10-1 = 1/10
1/10 = 0.1 
hundredths
10-2 = 1/102
1/102 = 0.01 
thousandths
10-3 = 1/103
1/103 = 0.001 
ten thousandths
10-4 = 1/104
1/104 = 0.0001 
hundred thousandths
10-5 = 1/105
1/105 = 0.00001 
millionths
10-6 = 1/106
1/106 = 0.000001 
billionths
10-9 = 1/109
1/109 = 0.000000001 
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