## Thinking Mathematically (6th Edition)

$6.47\times {{10}^{-7}}$.
Any real number in the form $a\times {{10}^{n}}$ is said to be in the scientific notation, where $1\le a<10$, and n is any integer. Since, the provided real number $0.000000647$is less than $1$, so n must be negative in the scientific notation $a\times {{10}^{n}}$. To determine the value of a, move the decimal point from left to right in the provided real number $0.000000647$, as provided number is less than $1$. So, $a=6.47$. Again, the decimal point moves $7$ places right in $0.000000647$, so$n=-7$. Hence the scientific notation of the real number $0.000000647$is $6.47\times {{10}^{-7}}$. Expression of $0.000000647$in scientific notation is $6.47\times {{10}^{-7}}$.