Calculating with Standard Form

Calculating with Standard Form

To add or subtract numbers in standard form, write the numbers so that they both have the same power of 10:

4.61 x 103 + 1.22 x 104

= 4.61 x 103 + 12.2 x 103 (both numbers to the same power of 10)

= (4.61 + 12.2) x 103

= 16.81 x 103 (add the two decimal numbers together)

= 1.681 x 104 (convert the number back into standard form).

The calculation could have been completed in other ways for the same answer eg by converting both numbers to be x 104, or by converting both numbers to normal form, adding them and converting back to standard form.

To be in standard form, the integer part must be greater than or equal to 1 and less than 10.

To multiply or divide numbers in standard form, multiply the decimal parts together; and use the laws of indices to multiply the powers of 10 together.

For example, (8.44 x 103) x (4.2 x 102):

= 8.44 x 4.2 x 103 x 102

= 35.488 x 105

= 3.5488 x 106 (convert back to standard form).

Example 1

The earth orbits the sun at a speed of about 7 x 105 miles per hour. There are approximately 9000 hours in a year. Write the distance travelled by the earth in a year in standard form.

7 x 105 x 9 x 103

= 7 x 9 x 105 x 103

= 63 x 108

= 6.3 x 109

Example 2

Add 5.87 x 10-3 and 2.66 x 10-2.

5.87 x 10-3 + 2.66 x 10-2

=5.87 x 10-3 + 26.6 x 10-3 (make both the powers of 10 the same)

=32.47 x 10-3

=3.247 x 10-2 (convert back to standard form)