Is there a simple formula when for getting the right sig-digs?

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In summary, the conversation discusses the difficulty of finding the correct number of significant digits when dealing with complex equations involving addition, subtraction, multiplication, and division. The speaker shares their thought process for solving such equations, but acknowledges that there may be an intermediate step that they are missing. The conversation also mentions a sign error in the initial step and clarifies the correct use of PEMDAS to arrive at the correct number of significant digits.
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student34
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Homework Statement



I have no problem knowing how to find the right sig-digs when just doing one of: adding, subtracting, multiplying or dividing. But, I know doing them all at once in more complicated equations gets trickier.

For example, something like 110.0 + (500434.0 - 34.0)/0.37

Homework Equations


The Attempt at a Solution



This is my thought process for finding sig-digs when addition/subtraction is combined with multiplication/division. The answer may be correct by luck, but I know that this is not the right way to come up with the correct number of sig-digs.

110.0 + (500434.0 - 34.0)/0.37
= 110.0 + 500434.0/0.37
= 110.0 + 1.4*10^6 (I make 500434/0.37 equal 2 sig digs because the denominator only has 2 sig-digs.)
= 1.4001100*10^6 (Then I increase the sig-digs by 5 because I am adding 110.0.)

I know this process is wrong because my professor tried to explain to me that there is an intermediate step that I am missing. I can't grasp what it is though.

If it is correct, it is because of pure luck.
 
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  • #2
You made a sign error in the very first step. You should fix that first.
 
  • #3
vela said:
You made a sign error in the very first step. You should fix that first.

Thanks, I meant to put 5400 - 34 instead of 34 - 5400, so I can use both + and - in the example.
 
  • #4
How did you go from ##110 + 1.3437\times10^5## to ##111.3437\times10^5##? Remember PEMDAS.
 
  • #5
vela said:
How did you go from ##110 + 1.3437\times10^5## to ##111.3437\times10^5##? Remember PEMDAS.

I don't know why I am so careless today (it's very frustrating being in university and not knowing this yet.).

I changed the question too.
 

1. What is a significant figure?

A significant figure is a digit that contributes to the precision of a number. It represents the number of digits that convey meaningful information in a number.

2. Why is it important to use the correct number of significant figures?

Using the correct number of significant figures is important because it ensures that the calculated value is as precise as the original values used in the calculation. It also helps to avoid errors and inaccuracies in scientific measurements and calculations.

3. How do you determine the number of significant figures in a number?

The rule for determining the number of significant figures in a number is that all non-zero digits are significant, all zeros between two significant digits are significant, and all final zeros to the right of a decimal point are significant. Additionally, if a number is in scientific notation, all digits in the coefficient are significant.

4. What is the significance of trailing zeros in a number?

Trailing zeros at the end of a number are only significant if there is a decimal point present. For example, 200 has one significant figure, but 200.00 has five significant figures. Trailing zeros without a decimal point are assumed to be placeholders and are not significant.

5. Is there a simple formula for determining significant figures?

There is no single formula for determining significant figures as it depends on the rules mentioned in the answer to question 3. However, a general guideline is to count the number of digits that convey meaningful information and consider them as significant figures.

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