# Significant Figures: Dealing With Simple Calculations

• myxomatosii
In summary, the student has completed the majority of the assignment and has received a score of 91.66/100. However, they are struggling with two problems that involve significant figures, denoted as (c) and (d). They have made multiple attempts at these problems and have not been successful. They have also searched for examples and methods, but still do not understand where they are going wrong. The student mentions that the significant figure rules seem to apply differently for conversions, where they are able to use as many decimal places as they want. They are hoping to receive assistance before the assignment is due on Friday night.
myxomatosii
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

## 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:
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.

First of all, don't feel pathetic for struggling with significant figures. They can be confusing and it's always better to ask for help when you're not sure. Let's go through the steps for solving these problems and hopefully we can figure out where you went wrong.

For (c), the problem is asking for the difference between 27.5 and 1.9. The answer should be 25.6, which you already tried. So that is the correct answer. I'm not sure why it's not being accepted, but it could be a technical error or a problem with the input format. I would recommend reaching out to your instructor or TA for assistance in this case.

For (d), the problem is asking for the value of 1 divided by 33.5. In this case, the answer should be 0.03. Again, I'm not sure why your attempts are not being accepted. It could be a technical issue or a problem with the input format. I would suggest reaching out to your instructor or TA for help with this problem as well.

In general, when dealing with significant figures, it's important to remember the rules for rounding and counting significant figures. For multiplication and division, the result should have the same number of significant figures as the number with the fewest significant figures. For addition and subtraction, the result should have the same number of decimal places as the number with the fewest decimal places. Also, when taking logarithms, the number of decimal places in the result should match the number of significant figures in the original number.

I hope this helps and good luck with your remaining attempts! Don't hesitate to reach out for help if you're still having trouble.

## 1. What are significant figures?

Significant figures, also known as significant digits, are the digits in a number that contribute to its precision. They include all non-zero digits and any zeros between non-zero digits.

## 2. How do I determine the number of significant figures in a number?

To determine the number of significant figures, start counting from the first non-zero digit and continue until the last non-zero digit. Zeros before the first non-zero digit are not significant, while zeros after the last non-zero digit may or may not be significant depending on the context.

## 3. How do I perform calculations with significant figures?

When performing addition or subtraction, the result should have the same number of decimal places as the number with the least number of decimal places. When performing multiplication or division, the result should have the same number of significant figures as the number with the least number of significant figures.

## 4. What is the purpose of using significant figures?

Significant figures are used to indicate the precision or accuracy of a number. They help to avoid misleading or overly precise results in calculations.

## 5. Can significant figures be applied to all types of numbers?

No, significant figures are typically used for measurements or experimental data. They are not typically used for counting numbers, exact values, or conversion factors.

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