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Scientific Notation

Converting From Scientific Notation to Expanded Form

Here’s how to convert a number from scientific notation to expanded form.

Procedure — To Convert From Scientific Notation to Expanded Form

Move the decimal point the same number of places as the exponent of 10.

• If the exponent is positive, move the decimal point right.

• If the exponent is negative, move the decimal point left.

As a check, note the following:

• If the power of 10 is positive, the number written in expanded form will be greater than or equal to 10.

• 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 × 1012 miles.

Write in expanded form: 5.87 × 1012

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 × 1012 in expanded form, we append 10 zeros (not 12).

 

Example 2

The gravitational force of attraction between two masses, m1 and m2, that are a distance r apart is given by

The G in the formula represents the universal gravitational constant,

Write 6.673 × 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,

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