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, 2,890,000,000 becomes 2.89 x 109. How?

  • Remember that any whole number can be written with a decimal point. For example: 2,890,000,000 = 2,890,000,000.0
  • 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.
  • 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.

  • 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.
  • 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.
Powers of Ten
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

Powers and ExponentsTables and FormulasFactorials

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