Question

How to simplify `(6.3 times 10^5) ÷ (9 times 10^3)` in scientific notation?

Answer 1

`7.0xx10`

Explanation:

`6.3xx10^5` is the same value as `63xx10^4`

So we have:

`(63xx10^4)/(9xx10^3) color(white)("ddd") -> color(white)("ddd") 63/9xx10^4/10^3`

`color(white)("ddddddddd.d")->color(white)("ddd")63/9xx10`

If the sum of the digits is exactly divisible by 3 then the actual number is also exactly divisible by 3 `->6+3=9` so we will divide both top and bottom by 3 to simplify the fraction.

`color(white)("ddddddddd.d")->color(white)("ddd")(63-:3)/(9-:3)xx10`

Note that:

`(63-:3)/(9-:3)=(21-:3)/(3-:3)=7/1=7` so we have:

`(6.3xx10^5)-:(9xx10^3) =7.0xx10`