Calculating with Standard Form

Calculating with Standard Form

GCSE(F), GCSE(H),

To add or subtract numbers in standard form, write the numbers with the same power of 10:

4.61 x 103 + 1.22 x 104

= 4.61 x 103 + 12.2 x 103 (convert 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.

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).

Examples

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.

Answer: 6.3 x 109

7 x 105 x 9 x 103

= 63 x 108

= 6.3 x 109.

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

Answer: 3.247 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)