Sig Fig Question Homework: What's Wrong?

[ThatDude]

Homework Statement

So basically, for a lab, I have to make a calculation abiding by the rules of sig figs, and it involves the subtraction of two numbers in scientific notation:

1.00 x10^-3 - 4.35 x10^-5

= 1.00 x10^-3 - 0.0435 x10^-3 ; therefore, we should round the final answer to two decimal places... which equals 9.57 x10^-4

But, when I do it the long way, like 0.00100 - 0.0000435, I get 0.0009565, this means we should round to 5 digits after the decimal point (from 0.00100), therefore the answer should be 9.6 x 10^-4.

So, both methods give me different values, where am I going wrong?

 

[RUber]

When you wrote it out in terms of the largest number, you were at 10^(-3), so round to 2 digits in that place--then adjust for scientific notation, and you will end up with the same result you found "the long way".

 

[Borek]

0.00100
0.0000435-
0.0009565

Last two digits you get after subtraction (65) make no sense - you know nothing about what 35 was subtracted from. Final answer can be - at best - of the
0.000XX form.

Don't worry too much about sigfigs, while they are better than nothing when it comes with reporting accuracy, they are not used anywhere outside of the school.