A number written in scientific notation consists of a coefficient which is greater than or equal to 1 and less than 10. It is multiplied by an integer power of 10.
To multiply two numbers in scientific notation together, we multiply the coefficients together. Then we multiply the powers of 10 together. We may then need to do some adjusting in case the new coefficient falls outside the range of accepted values, for example, if the new coefficient is less than 1 or greater than or equal to 10.
In this multiplication, the coefficients are 4 and 1.4. The integer powers of 10 are 10^-7 and 10^-7. We use the commutative and associative properties of multiplication to change the order and grouping of the factors.
[tex] (4 \times 10^{-7})(1.4 \times 10^{-7}) = [/tex]
[tex] = 4 \times 10^{-7} \times 1.4 \times 10^{-7} [/tex]
[tex] = 4 \times 1.4 \times 10^{-7} \times 10^{-7} [/tex]
[tex] = (4 \times 1.4) \times (10^{-7} \times 10^{-7}) [/tex]
[tex] = 5.6 \times 10^{-7 + (-7)} [/tex]
[tex] = 5.6 \times 10^{-14} [/tex]
The coefficient is in the correct range, from 1 to less than 10, so there is no need for adjustment. The last line above is the answer.
