# Math Help - Significant digit? how to work this out?

1. ## Significant digit? how to work this out?

Hi.

I would like to ask those that have done a bit on computational Maths.
I thought I understood it but my lecture notes gives another example and i don't get it:

actual value = 23.496 and estimate = 23.494
The the error is |actual - estimate|= 0.002.
The actual value has four signifi cant digits with respect to actual value , since the error is less
than 5 in the fifth place to the right of the first nonzero digit in actual . Note that if estimate
is rounded to four places, an additional error is introduced and estimate will no longer have four signi ficant digits.

What does even this mean? I don't get it. Please someone explain for me.

2. ## Re: Significant digit? how to work this out?

Originally Posted by willy0625
Hi.

I would like to ask those that have done a bit on computational Maths.
I thought I understood it but my lecture notes gives another example and i don't get it:

actual value = 23.496 and estimate = 23.494
The the error is |actual - estimate|= 0.002.
The actual value has four significant digits with respect to actual value , since the error is less
than 5 in the fifth place to the right of the first nonzero digit in actual . Note that if estimate
is rounded to four places, an additional error is introduced and estimate will no longer have four significant digits.

What does even this mean? I don't get it. Please someone explain for me.
I don't get it either but there are a large numbers of ways to do this. Check with your instructor. I would say your answer should be: $23.494 \pm 0.002$.

-Dan

3. ## Re: Significant digit? how to work this out?

This is his definition:

In place of relative error, we often use the concept of signifi cant digits. we say estimate has m
signifi cant (decimal) digits with respect to actual if the error (actual - estimate) has magnitude less
than or equal to 5 in the (m+1)st digit of actual , counting to the right from the first nonzero
digit in actual .

Does it help?