# How do you write 0.00000000016 in scientific notation?

Jul 25, 2016

$0.00000000016 = 1.6 \times {10}^{- 10}$

#### 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 $a \times {10}^{n}$, where $1 \le a < 10$ 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 $0.00000000016 = 1.6 \times {10}^{- 10}$ (note that as we have moved decimal one point to right we are multiplying by ${10}^{- 10}$.

Jul 25, 2016

$0.00000000016 = 1.6 \times {10}^{-} 10$

#### Explanation:

The solution

$0.00000000016 = 1.6 \times {10}^{-} 10$

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

$0.00000000016 = 1.6 \times {10}^{-} 10$

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