Scientific Notation
Converting From Scientific Notation to Expanded Form
Hereâ€™s how to convert a number from scientific notation to expanded form.
Procedure â€”
To Convert From Scientific Notation to Expanded Form
Move the decimal point the same number of places as the exponent
of 10.
â€¢ If the exponent is positive, move the decimal point right.
â€¢ If the exponent is negative, move the decimal point left.
As a check, note the following:
â€¢ If the power of 10 is positive, the number written in expanded
form will be greater than or equal to 10.
â€¢ If the power of 10 is negative, the number written in expanded
form will be greater than 0 and less than 1.
Example 1
A light year is a measure of distance.
Its value is approximately 5.87 Ã— 10^{12} miles.
Write in expanded form: 5.87 Ã— 10^{12}
Solution
The exponent, 12, is positive, so move the
decimal point 12 places to the right.
As you move the decimal point, you will have
to append zeros to the right of 587 to serve as
place holders.
The result is: 5,870,000,000,000
A light year is almost 6 trillion miles.
Note:
Be careful! The power of 10 does NOT tell
us how many zeros to append to the right
of the number.
To write 5.87 Ã— 10^{12} in expanded form,
we append 10 zeros (not 12).
Example 2
The gravitational force of attraction between two masses, m_{1} and m_{2},
that are a distance r apart is given by
The G in the formula represents the universal gravitational constant,
Write 6.673 Ã— 10^{11} in expanded form.
Solution
The exponent, 11, is negative, so move the decimal point 11 places to
the left.
As you move the decimal point, you will have to append zeros to the left
of 6673 to serve as place holders.
Thus,
