Question

Another Algebra question I can't understand!

Answer 1

Answer:

$6.180 \cdot 10^{-5}$

Step-by-step explanation:

So I'm going to separate the fraction like so:

$\frac{3.3 \cdot 10^2}{5.34 \cdot 10^6}=\frac{3.3}{5.34} \cdot \frac{10^2}{10^6}$

I'm going to do the 3.3 divided by 5.34 in my calculator.

3.3/5.34 is equal to 0.6179775 (approximately).

I'm going to use law of exponents to simplify: $\frac{10^2}{10^6}$.

When you are dividing by the same based number, you subtract the exponents. So you will keep the same based number and your exponent will be top exponent minus bottom exponent. Like this:

$\frac{10^2}{10^6}=10^{2-6}=10^{-4}$.

So this is what we have right now before moving on.

The answer is approximately $0.6179775 \cdot 10^{-4}$.

In order for this to be in scientific notation we need the first number to be between 1 and 10 (not including 10). To do this, we move the decimal either left or right depending where it is and change the factor of 10.

So 0.6179775 only needs to have the decimal moved over once to the right so 0.6179775 is $6.179775 \cdot 10^{-1}$

The exponent of -1 came form us moving it right once.

So now this is what we have so far:

$6.179775 \cdot 10^{-1} \cdot 10^{-4}$

I brought down the 10^(-4) form earlier because I was focusing on the the other part to be in scientific notation.

So if you have the same based number when multiplying, you add the exponents like so:

$6.179775 \cdot 10^{-1+-4}$

$6.179775 \cdot 10^{-5}$

Now I didn't worry about the 4 significant digits until now.

We want the first 4 digits reading the number from left to right on our first number.

$6.180 \cdot 10^{-5}$

I rounded because the 5th digit was 5 or more.