GCSE(F), GCSE(H),

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

4.61 x 10^{3} + 1.22 x 10^{4}

= 4.61 x 10^{3} + 12.2 x 10^{3} (convert both numbers to the same power of 10)

= (4.61 + 12.2) x 10^{3}

= 16.81 x 10^{3} (add the two decimal numbers together)

= 1.681 x 10^{4} (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 10^{3}) x (4.2 x 10^{2}):

= 8.44 x 4.2 x 10^{3} x 10^{2}

= 35.488 x 10^{5}

= 3.5488 x 10^{6} (convert back to standard form).

1. The earth orbits the sun at a speed of about 7 x 10^{5} 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 10^{9}

7 x 10^{5} x 9 x 10^{3}

= 63 x 10^{8}

= 6.3 x 10^{9}.

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)

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