Significant Figures: Dealing With Simple Calculations

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SUMMARY

The discussion focuses on the application of significant figures in calculations, specifically in a homework assignment involving operations such as subtraction and division. The user successfully completed parts (a) and (b) but struggles with parts (c) and (d), having made multiple incorrect attempts. The significant figure rules outlined in the textbook emphasize that the result of calculations should reflect the precision of the least precise operand, which is critical for accurate scientific communication.

PREREQUISITES
  • Understanding of significant figures and their importance in scientific calculations
  • Familiarity with basic arithmetic operations (addition, subtraction, multiplication, division)
  • Knowledge of scientific notation for expressing significant figures
  • Ability to interpret and apply guidelines from educational resources like WebAssign
NEXT STEPS
  • Review the rules for significant figures in subtraction and division
  • Practice converting numbers to scientific notation to express significant figures accurately
  • Explore examples of significant figures in logarithmic calculations
  • Investigate common pitfalls in significant figure applications in homework platforms like WebAssign
USEFUL FOR

Students in mathematics or science courses, educators teaching significant figures, and anyone needing to improve their understanding of precision in numerical calculations.

myxomatosii
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EDIT: I finished the assignment other than the two problems listed here, I got 91.66/100 but would love those last 8.44 points, I'll be checking in on this topic Thursday afternoon and might have figured it out by then but I am wary to waste my last attempt. So.. that's the update

Ok throughout the years maybe I just haven't had a good explanation of significant figures teacher to teacher year to year and I do feel a bit pathetic posting such a simple "problem" but nonetheless here is my situation.

I have five tries at each problem, and after looking up example after example and method after method I have gotten parts (a) and (b) correct but am left with (c) with one more attempt and (d) with two more attempts.

My four attempts at (c) which were all wrong were: "26", "26.0", "25.6", "25." and with one more attempt at it I have no idea what they want from me as they give me no decent explanation to what I am doing wrong.

My three attempts at (d) which were all wrong were: "0.03", ".03", and "0." with two more attempts, and I really cannot think of anything else to try and as I said it gives no decent explanation and I do not want to throw away another try until I can talk to someone to see what my problem is.


Homework Statement



Compute the following numbers, applying the significant figure rules adopted in this textbook.

(a) 27.5^2
(b) 32.9 * 21.3
(c) 27.5 - 1.9
(d) 1/33.5

Homework Equations



None. Significant figure guidelines. (Taken from assignment and pasted below.)

Using Significant Figures in WebAssign
Significant figures are one way of expressing uncertainty in measurement. The rules WebAssign uses to determine the number of significant figures in a number are shown in the examples below:

1234 = 4 significant figures 5.0e2 = 2 significant figures
500 = 1 significant figure 140E-001 = 2 significant figures
500. = 3 significant figures 8.20000e3 = 6 significant figures
13000 = 2 significant figures 101.001 = 6 significant figures
2.000 = 4 significant figures 41003 = 5 significant figures

As you can see, most numbers are fairly straightforward.
To express a number like 1000 to 2 or 3 significant figures, you must use scientific notation.

When you multiply or divide numbers, the result of your calculation has the same number of significant digits as the operand with the fewest number of significant figures. For example:

1530 4.0 = 6100
1530 (3 significant figures) 4.0 (2 significant figures) = 6100 (2 significant figures)

When you add or subtract numbers, keep the fewest number of decimal places that are in all of the numbers. For example:

2.46 + 6.1743 = 8.63
2.46 (to the hundredths place) + 6.1743 (to the ten-thousandths place) = 8.63 (to the hundredths place)

4580 - 411 = 4170
4580 (to the tens place) - 411 (to the ones place) = 4170 (to the tens place)

When you take the logarithm of a number, the number of decimal places in the result must be the same as the number of significant figures in the number you started with (Why is this?). For example:

log10(27) = 1.43
log10(27 two significant figures) = 1.43 (two decimal places)

ln(0.026) = -3.65
Keep in mind that certain numbers are considered to be absolute, such as the coefficients in the chemical formula below (for example, the 3).

3 H2 + 2 C = C2H6

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The Attempt at a Solution




I have five tries at each problem, and after looking up example after example and method after method I have gotten parts (a) and (b) correct but am left with (c) with one more attempt and (d) with two more attempts.

My four attempts at (c) which were all wrong were: "26", "26.0", "25.6", "25." and with one more attempt at it I have no idea what they want from me as they give me no decent explanation to what I am doing wrong.

My three attempts at (d) which were all wrong were: "0.03", ".03", and "0." with two more attempts, and I really cannot think of anything else to try and as I said it gives no decent explanation and I do not want to throw away another try until I can talk to someone to see what my problem is.
 
Last edited:
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I've continued to do the other problems given in the same homework assignment and none of the same rules seem to apply.

Is it because they are conversions? IE: Convert kg/cm^3 to kg/m^3 (etc)
And those numbers are known absolutely? Because I seem to be able to go to as many decimal places as I want on those problems and it accepts my answer, I was wary and now I just realize it accepts any # of decimals, I don't get it.. arg, when does it apply and when does it not?

Anyway I'm pretty much done with the assignment other than the two problems with sig figs I posted above and it is not due until Friday night so hopefully one of you can help me before then.
 

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