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
