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Question
Represent the following numbers in scientific notation:
`{(0.00003)^6 xx (0.00005)^4} ÷ {(0.009)^3 xx (0.05)^2}`
Solution
`{(0.00003)^6 xx (0.00005)^4} ÷ {(0.009)^3 xx (0.05)^2}`
= `((3.0 xx 10^(-5))^6 xx (5.0 xx 10^(-5))^4)/((9.0 xx 10^(-3))^3 xx (5.0 xx 10^(-2))^2`
= `((3.0)^6 xx (10^(-5))^6 xx (5.0)^4 xx (10^(-5))^4)/((9.0)^3 xx (10^(-3))^3 xx (5.0)^2 xx (10^(-2))^2`
= `(729 xx 10^(-30) xx 625 xx 10^(-20))/(729 xx 10^(-9) xx 25 xx 10^(-4)`
= `(625 xx 10^(-30) xx 10^(-20))/(25 xx 10^(-9) xx 10^(-4)`
= `(25 xx 10^(-30 - 20))/(10^(-9 - 4))`
= `(25 xx 10^(-50))/(10^(-13))`
= `(2.5 xx 10 xx 10^(-50))/(10^(-13))`
= `(2.5 xx 10^(-49))/(10^(-13))`
= `2.5 xx 10^(-49 + 13)`
= 2.5 × 10−36
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