Fraction With Scientific Notation As A Percentage

Question

I have this fraction $\frac{3.09\times 10^{-9}}{0.02\times 10^{-9}}$ and I need to convert it to a percentage. What I do know is that the $10^{-9}$ cancels out and we are left with $\frac{309}2$, but converting this to a percentage yields a weird number, $15450\%$.

Is this number $15450\%\times 10^{-9}$ or it is simply the $15450\%$? How can the negative values equal a positive number? I'm a little confused.

Thanks for answering.

Answer 1

First, you don't have any negative numbers here. $3.09 \times 10^{-9}$ really means $3.09 \times 0.0000000001$. These are both positive numbers. $10^{-9}$ is just a very small positive number.

When working with fractions, the percentage tells you how many times the denominator fits into the numerator. 10/4 = 250% because 4 fits into 10 2.5 times. The reason you got a large percentage is because 2 fits into 309 154.5 times, which is the same as 15450%.

So the large percentage you got looks a little weird but it's correct.

Answer 2

There is no negative number. The ratio 3.09/.02 = 302/2 right? So why would it be any different if there are 9 more zeros? That's what the scientific notation means. Percentages can be more than 100. That means that there are more things than a 100 per one hundred.