Question

How do you write `0.00000000016` in scientific notation?

Answer 1

`0.00000000016=1.6xx10^(-10)`

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`.

Note that moving decimal `p` digits to right is equivalent to multiplying by `10^p` and moving decimal `q` digits to left is equivalent to dividing by `10^q`.

Hence, we should either divide the number by `10^p` i.e. multiply by `10^(-p)` (if moving decimal to right) or multiply the number by `10^q` (if moving decimal to left).

In other words, it is written as `axx10^n`, where `1<=a<10` and `n` is an integer.

To write `0.00000000016` in scientific notation, we will have to move the decimal point ten points to right, which literally means multiplying by `10^10`.

Hence in scientific notation `0.00000000016=1.6xx10^(-10)` (note that as we have moved decimal one point to right we are multiplying by `10^(-10)`.

Answer 2

`0.00000000016=1.6 xx 10^-10`

Explanation:

The solution

`0.00000000016=1.6 xx 10^-10`

The exponent `-10` is obtained by counting the number of zeros to the right of the decimal point plus one.

So the decimal point is place in between 1 and 6 so that it is written `1.6` , then multiplying it by `10^(-10)`

So we write the final scientific notation

`0.00000000016=1.6 xx 10^-10`

God bless....I hope the explanation is useful.