WRITING A NUMBER IN SCIENTIFIC NOTATION

To translate between standard notation and scientific notation, you can count the number of places the decimal point moves.

To write a number which is greater than 1 in scientific notation, move the decimal point left and use a positive exponent.

It has been illustrated in the picture given below.

To write a number which is less than 1 in scientific notation, move the decimal point right and use a negative exponent.

It has been illustrated in the picture given below.

Solved Examples

Example 1 : 

The distance from Earth to the Sun is about 93,000,000 miles. Write this distance in scientific notation.

Solution : 

Step 1 :

Move the decimal point in 93,000,000 to the left until you have a number that is greater than or equal to 1 and less than 10.

Move the decimal point 7 places to the left.

Remove extra zeros.

9.3

Step 2 :

Divide the original number by the result from Step 1.

That is, divide 93,000,000 by 9.3.

10,000,000

Write your answer as a power of 10.

10⁷

Step 3 :

Write the product of the results from Steps 1 and 2.

Write a product to represent 93,000,000 in scientific notation.

93,000,000  =  9.3 × 10⁷ miles

Example 2 : 

The average size of an atom is about 0.00000003 centimeter across. Write the average size of an atom in scientific notation.

Solution : 

Step 1 :

Move the decimal point as many places as necessary to find a number that is greater than or equal to 1 and less than 10.

Place the decimal point after 3 and put one zero to make the decimal visible. 

3.0

Step 2 :

Count the number of places you moved the decimal point.

8

Step 2 :

Multiply 3.0 times a power of 10.

Since 0.00000003 is less than 1, you moved the decimal point to the right and the exponent on 10 is negative.

3.0 × 10^-8

The average size of an atom in scientific notation is 3.0 × 10^-8.

Reflect

When we write a number that is less than 1 in scientific notation, how does the power of 10 differ from when we write a number greater than 1 in scientific notation ?

The exponent is negative instead of positive.

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