Math help - and this is NOT homework.

Tonyr1084 said:

I see that this works. But I don't understand why. Why is 333e-6/0.7/10e-9 the same as 333e-6/(0.7•10e-9)? What changes? I understand the parenthesis, but don't understand why removing them and changing the function from multiplication to devision works.

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This is the fraction that you're trying to simplify:
\( \small R2 = \frac{333e-6}{0.7*10e-9}\)
which can also be written as:
\( \small R2 = \frac{333e-6}{(0.7*10e-9)} \)
because all of the operations in the denominator must be kept together.

What you're inclined to do is this:
\( \small R2 = \frac{333e-6}{0.7}*10e-9 \)
which is wrong. While this would be correct:
\( \small R2 = \frac{333e-6}{0.7}*\frac{1}{10e-9}\)

You could have saved yourself a grab for a calculator if you did the multiply of the denominator in your head, observed that 333 is close to 350, did the division of 350/7 in your head, cancelled the exponents so you had e-3 in the denominator, and arrive at 50e3 as an approximate answer. Knowing you rounded the time up, round down to the next standard value. Which would be 47k if you used 5% tolerance resistors.

EDIT: corrected usage of numerator, should have been denominator as in earlier posts.

Ratio with approximations:
\( \small R2 = \frac{350e-6}{7e-9}=\frac{350}{7e-3}=\frac{50}{1e-3}=50e3\)