Question

convert the following measurement.
7.6×10²\frac{mg}{dl}=\square\frac{g}{l}

Explanation:

Step1: Convert milligrams to grams

Since \(1\space g = 1000\space mg\), then \(1\space mg=\frac{1}{1000}\space g = 10^{- 3}\space g\). So \(7.6\times10^{2}\space mg=7.6\times10^{2}\times10^{-3}\space g\).
Using the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\), we have \(7.6\times10^{2}\times10^{-3}=7.6\times10^{2-3}=7.6\times10^{-1}\space g\).

Step2: Convert deciliters to liters

Since \(1\space L = 10\space dL\), then \(1\space dL=\frac{1}{10}\space L=10^{-1}\space L\).
The original expression \(\frac{7.6\times 10^{2}\space mg}{1\space dL}\) becomes \(\frac{7.6\times10^{-1}\space g}{10^{-1}\space L}\).
Using the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\), \(\frac{7.6\times10^{-1}}{10^{-1}}=7.6\times10^{-1-( - 1)}=7.6\times10^{0}\).
Since \(a^{0}=1\) (\(a
eq0\)), \(7.6\times10^{0}=7.6\).

Answer:

\(7.6\)