scientific notation
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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 10^{9}. 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 10^{9}.
2.89 x 10^{9} = 2.89 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10
2.89 x 10^{9} = 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 exponentthe small number
above and to the right of the 10tells which way you moved the
decimal point.
A power of ten with a positive exponent, such as 10^{5},
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.

Powers of Ten

billions
10^{9} = 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
10^{6} = 1,000,000
10 x 10 x 10 x 10 x 10 x 10 = 1,000,000
hundred thousands
10^{5} = 100,000
10 x 10 x 10 x 10 x 10 = 100,000
ten thousands
10^{4} = 10,000
10 x 10 x 10 x 10 = 10,000
thousands
10^{3} = 1,000
10 x 10 x 10 = 1,000
hundreds
10^{2} = 100
10 x 10 = 100
tens
10^{1} = 10
ones
10^{0} = 1
tenths
10^{1} = 1/10
1/10 = 0.1
hundredths
10^{2} = 1/10^{2}
1/10^{2} = 0.01
thousandths
10^{3} = 1/10^{3}
1/10^{3} = 0.001
ten thousandths
10^{4} = 1/10^{4}
1/10^{4} = 0.0001
hundred thousandths
10^{5} = 1/10^{5}
1/10^{5} = 0.00001
millionths
10^{6} = 1/10^{6}
1/10^{6} = 0.000001
billionths
10^{9} = 1/10^{9}
1/10^{9} = 0.000000001

