Question

How do you convert `4.9xx10^-7` to standard form?

Answer 1

In standard form `4.9xx10^(-7)=0.00000049`

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, in scientific notation, a number is written as `axx10^n`, where `1<=a<10` and `n` is an integer and `1<=a<10`.

To write the number in normal or standard notation one just needs to multiply by the power `10^n` (or divide if `n` is negative). This means moving decimal `n` digits to right if multiplying by `10^n` and moving decimal `n` digits to left if dividing by `10^n` (i.e. multiplying by `10^(-n)`).

In the given case, as we have the number as `4.9xx10^(-7)`, we need to move decimal digit to the left by seven points. For this, let us write `4.9` as `000000049` and moving decimal point seven points to the left means `0.00000049`

Hence in standard form `4.9xx10^(-7)=0.00000049`

Answer 2

`4.9xx10^(-7) = 0.00000049`

Explanation:

`4.9xx10^(-7)` is the same as `4.9xx1/(10^7)`

Taking it stepwise so that you can see what is happening:

`4.9xx1/10^7`

`0.49xx1/10^6`

`0.049xx1/10^5`

`0.0049xx1/10^4`

`0.00049xx1/10^3`

`0.000049xx1/10^2`

`0.0000049xx1/10^1`

`0.00000049xx1/10^0`

But `1/10^0 = 1/1 = 1` giving

`0.00000049xx1 " "=" "0.00000049`

So `4.9xx10^(-7) = 0.00000049`