Question

How do you work out the value of `(7.5 times 10^4) times (2.5 times 10^3)` in standard form?

Answer 1

`(7.5xx10^4)xx(2.5xx10^3)=1.875xx10^8`

Explanation:

In scientific notation, we write a number so that it has single digit to the left of decimal sign and is multiplied by an integer power of `10`. In other words, it is written as `axx10^n`, where `1<=a<10` and `n` is an integer.

Hence, we should write `(7.5xx10^4)xx(2.5xx10^3)` as

`7.5xx2.5xx10^4xx10^3`

= `18.75xx10^((4+3))`

= `18.75xx10^7`

Now as we should have a number with single digit, we should write `18.75` as `1.875xx10` and

`1.875xx10xx10^7`

= `1.875xx10^((1+7))`

= `1.875xx10^8`