To solve this question, we must first write it out:
[tex] \frac{4.2* x10^{2} }{6.72* 10^{4} } [/tex]
Then we can first take the numbers, and divide them:
[tex] \frac{4.2}{6.72}=0.625 [/tex]
Then we take the rest of the equation and solve. When you have the same term raised to an exponent, you subtract the denominator's exponent from the numerator's exponent to find the final term's exponent. Also, if an exponent comes out to be negative, flip the exponent to the bottom. Let's solve following that method:
[tex] \frac{ 10^{2} }{ 10^{4} }= 10^{-2}= \frac{1}{10^{2} } [/tex]
So, now you have two terms: 0.625 and [tex] \frac{1}{ 10^{2} } [/tex] or [tex] \frac{1}{100} [/tex]
So now we can multiply them together:
[tex] \frac{0.625}{1} * \frac{1}{100}= \frac{0.625}{100}=0.00625 [/tex]
Now we know that in scientific notation, we cannot leave the answer like this. Instead, the number has to be between 1 and 10. So, we need to move the decimal. When you move the decimal to the left, you add numbers to the exponent of the 10 (the 10 of the scientific notation), and when you move the decimal to the right, you subtract numbers from the exponent of the 10.
In this case, we are moving the decimal to the right 3 places so that we get 6.25. However, to compensate for the moving of the decimal, we are going to subtract 3 from the exponent of the 10 from scientific notation. This then gives us:
[tex]6.25* 10^{-3} [/tex]
