Question

convert the following measurement.
3.4 × 10^{-9} \frac{kg·m^{2}}{s^{2}} = \square \frac{g·cm^{2}}{s^{2}}

Explanation:

Step1: Convert kilograms to grams

Since \(1\space kg = 1000\space g=10^{3}\space g\), and \(1\space m = 100\space cm = 10^{2}\space cm\).
We have \(3.4\times 10^{-9}\frac{kg\cdot m^{2}}{s^{2}}=3.4\times 10^{-9}\times\frac{10^{3}\space g\times(10^{2}\space cm)^{2}}{s^{2}}\).

Step2: Simplify the expression

First, calculate \((10^{2})^{2}=10^{4}\). Then \(10^{3}\times10^{4}=10^{3 + 4}=10^{7}\).
So \(3.4\times 10^{-9}\times10^{7}\frac{g\cdot cm^{2}}{s^{2}}\).
Using the rule \(a^{m}\times a^{n}=a^{m + n}\), we get \(3.4\times10^{-9 + 7}\frac{g\cdot cm^{2}}{s^{2}}\).
\(3.4\times10^{-2}\frac{g\cdot cm^{2}}{s^{2}}=0.034\frac{g\cdot cm^{2}}{s^{2}}\).

Answer:

\(0.034\)