Question

Question #faff2

Answer 1

`(axx10^n)/(bxx10^m) = a/b xx 10^(n-m)`

Explanation:

Using the property of exponents that `x^a/x^b = x^(a-b)`, suppose `a xx 10^n` and `b xx 10^m` are two numbers in scientific notation (i.e. `a, b in [1, 10)`) Then

`(axx10^n)/(bxx10^m) =a/b xx 10^n/10^m = a/b xx 10^(n-m)`

Note that `1/10 < a/b < 10`, meaning an additional `10^(-1)` may be multiplied `10^(n-m)` if we are writing the answer in scientific notation.

Some examples:

`(6 xx 10^5)/(2 xx10^9) = 6/2 xx 10^(5-9) = 3 xx 10^-4`

`(2 xx 10^7)/(5xx10^3) = 2/5 xx 10^(7-3) = 0.4xx10^4 = 4xx10^3`