# Manual calculatioin accuracy???

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#### ocwaveoc

##### Membership Revoked
Removed
10+ Year Member

Hello everyone. I'm wondering how accurate manual calculation needs to be in order to get the right answer.
For an example:
15x10^-4J + 4.82x10^-4J / 8.5 x 10^-6C
When I add the numerator, I'm thinking 20 x 10^-4
Then, 20 x 10^-4 / 8.5 x 10^-6......which I'm thinking 20 x 10^-4 / 10 x 10^-6.
This gives me 200.....but, since I made the denomenator a bit larger in the previous step, I'll enlarge the answer a bit.......so the final answer is 220.
When you acually do the calculation on a calculator, the answer comes out to be 233.

To what degree do you suggest manual calculation to be accurate to? Please give an example.
Thanks!

#### estairella

##### Senior Member
10+ Year Member
A good rule of thumb: a quarter of the smallest division between the answers on the multiple choice.

For example, if the answers were:
a) 140
b) 170
c) 200
d) 230
e) 260

Your division is 30, so 30/4 = 7.5 and your estimates should land between 222.5-237.5

220 is pretty close. Personally, I would have done 20/9 instead of 20/10, the answer I'd get is 222+ (I know more because I up-rounded bottom more than I up-rounded top).

#### ocwaveoc

##### Membership Revoked
Removed
10+ Year Member
I see. Thanks for the reply.
However, after you determine how accurate you need to be, during the actual calculation, how do you ensure that the calculation is going to be within that range you set out for yourself?

A good rule of thumb: a quarter of the smallest division between the answers on the multiple choice.

For example, if the answers were:
a) 140
b) 170
c) 200
d) 230
e) 260

Your division is 30, so 30/4 = 7.5 and your estimates should land between 222.5-237.5

220 is pretty close. Personally, I would have done 20/9 instead of 20/10, the answer I'd get is 222+ (I know more because I up-rounded bottom more than I up-rounded top).

#### DrBowtie

##### Final Countdown
Moderator Emeritus
10+ Year Member
I found that it usually was just a matter of getting the right order of magnitude. Anything more than that was just insurance.