Question

(a) a certain solution has a hydrogen ion concentration of 6.53×10⁻⁴ moles per liter. write this number in standard notation. (b) a blue whale can weigh up to 420,000 pounds. write this number in scientific notation.

Explanation:

Step1: Convert scientific - notation to standard notation for (a)

For a number in scientific notation $a\times10^{-n}$ ($n>0$), we move the decimal point $n$ places to the left. Given $6.53\times 10^{-4}$, we move the decimal point 4 places to the left. So, $6.53\times 10^{-4}=0.000653$.

Step2: Convert standard notation to scientific notation for (b)

For a number $N$, scientific notation is of the form $a\times 10^{n}$, where $1\leqslant|a|<10$ and $n$ is an integer. For $420000$, we move the decimal point 5 places to the left to get $a = 4.2$ and $n = 5$. So, $420000=4.2\times 10^{5}$.

Answer:

(a) $0.000653$
(b) $4.2\times 10^{5}$