Question

answer the following.
(a) a certain solution has a hydrogen ion concentration of $6.53 \times 10^{-5}$ moles per liter. write this number in standard notation.
(b) a whale shark can weigh up to 47,000 pounds. write this number in scientific notation.
(a) \\(\square\\) moles per l.
(b) \\(\square\\) pounds

Explanation:

Step1: Convert \(6.53 \times 10^{-5}\) to standard notation

To convert a number in scientific notation \(a\times10^{n}\) to standard notation, if \(n\) is negative, we move the decimal point \(|n|\) places to the left. For \(6.53\times 10^{-5}\), \(n = - 5\), so we move the decimal point 5 places to the left.
\(6.53\times10^{-5}=0.0000653\)

Step2: Convert 47000 to scientific notation

To convert a number to scientific notation, we write it as \(a\times10^{n}\) where \(1\leqslant|a|\lt10\) and \(n\) is an integer. For 47000, we move the decimal point 4 places to the left to get \(a = 4.7\) and \(n=4\). So \(47000 = 4.7\times10^{4}\)

Answer:

(a) \(0.0000653\) moles per L
(b) \(4.7\times 10^{4}\) pounds