Chocolate sales totaled $3.01 x 108 in 2004. What is this in standard notation?
108 = 100,000,000
$3.01 x 100,000,000 = $301,000,000.
In other words, chocolate sales were $301 million in 2004.
An alternate method would be to recognize that 108 indicates eight place values. So, move the decimal eight places to the right, adding zeros and commas as needed.
Basically, you perform all of the steps backwards that you learned on the previous page.
To Write Scientific Notation in Standard Notation
Determine whether the exponent of 10 is greater than zero or less than zero.
If the exponent is greater than zero, move the decimal point to the right the same number of places as the exponent, adding as many zeros as you need for placeholders. Add commas, as needed, to indicate place value.
If the exponent is less than zero, move the decimal point to the left the same number of places as the exponent, adding as many zeros as you need for placeholders.
Example 1: Scientific Notation to Standard Notation
Change each to standard notation.
6.03 x 106
As the exponent is positive, move the decimal six places to the right, adding four zeros. Don't forget that the number in the tenths place (the zero) and the number in the hundredths place (the three) count as two of the six places that you move to the right.
5.3 x 10-4
As the exponent is negative, move the decimal four places to the left, adding three zeros. Don't forget that the number in the ones place (the five) counts as one of the four places that you move to the left.