Scientific Notation

Scientific NotationScientific notation is a means of reformatting very large or very small numbers so that there is not an abundance of leading or trailing place values (powers of 10.)  Many scientists deal with very large and/or very small numbers and need to write a shorthand notation for these numbers; therefore, the name scientific notation is appropriate.

To write a number in scientific notation is simple. Locate the decimal in the number and move it so that only one digit in the number is to the left of the decimal.  Next count how many place values the decimal was moved. It is necessary to replace those place values that were removed by powers of 10 where 10 is the base and the exponent is represented by counting how many place values were removed. If the decimal was moved to the left, then the exponent is positive; if the decimal was moved to the right, then the exponent is negative.

Example 1: Write 3400 in scientific notation

Rewrite the number as 3.400.  Notice that the decimal was moved 3 place values to the left, so the exponent would be +3.  To replace those place values (powers of 10) so that the new number is equivalent to 3400, it would be necessary to multiply 3.4 by1000 or 103
3400
. = 3.4 x 103

Example 2:  Write .00000678 in scientific notation

Rewrite the number as 6.78.  Notice that the decimal was moved 6 place values to the right, so the exponent would be -6.  To replace those place values (powers of 10) so that the new number is equivalent to 0.00000678, it would be necessary to multiply 6.78 by 10-6

.00000678 = 6.78 x 10-6

Changing a number from scientific notation to decimal (base 10) notation is reversing the above process. Once again the decimal in the number will be moved so that it will be all the way to the left of the number (for very small numbers) or all the way to the right (for very large numbers.)

Example 3:  Write 5.607 x 108 in decimal notation.  Think of this as making the number larger (since the exponent is positive) by replacing (moving the decimal to the right) 8 place values of 10 to the number
5
.607 x 108 = 560,700,000.

Notice (above) that 5 zeroes needed to be added to the end of the number since there were only 3 digits to the right of the decimal in the scientific notation number.

Example 4:  Write 8.092 x 10-5 in decimal notation.  Think of this as making the number smaller (since the exponent is negative) by removing (moving the decimal to the left) 5 place values of 10 to the number.

8.092 x 10-5 = .00008092

Notice (above) that 4 zeroes needed to be added to the beginning of the number since there was only 1 digit to the left of the decimal in the scientific notation number.

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The views and opinions expressed in this page are strictly those of Mary Lou Baker.
The contents of this page have not been reviewed or approved by Columbia State Community College.

This page was edited on 28-Jan-2013