Significant Figures in Mixed Operations Problem Driving Me Bonkers

[themuffinyamber]

So this is driving me crazy. In my Chemistry class, we are learning about retaining significant figures and digits of precision in problems with Mixed Operations. We are told not to round until the end, but to use superscripts to retain significant figures/digits of precision. I have submitted this answer and it was marked incorrect. PLEASE HALP!! Thank you!!!

0.5230 73.152 - 2.35
-------- - ---------------- * 5.72
1.2941 0.001

First I take care of my fractions:

0.5230/1.2941 = 0.4041⁴¹ (4 SFs retained)

73.152-2.35 = 70.80² (2 digits of precision retained)
70.80²/0.001 = 70802 (w/b 70000 for 1 SF)

Problem is now:

0.4041⁴¹ - 70000 ^(70802) * 5.72

Multiplication first:
70802 * 5.72 = 404987^.44 (0 digits of precision)

Then Subtraction:

0.4041⁴¹ - 404987^.44 = -404987.0359

-404987.0359 = -404987.04 (2 digits of precision)


I've tried submitting -404987.04 AND -404987 and both are incorrect. I can't figure it out! Ripping my hair out! Please help

 

[tkhunny]

So this is driving me crazy. In my Chemistry class, we are learning about retaining significant figures and digits of precision in problems with Mixed Operations. We are told not to round until the end, but to use superscripts to retain significant figures/digits of precision. I have submitted this answer and it was marked incorrect. PLEASE HALP!! Thank you!!!

0.5230 73.152 - 2.35
-------- - ---------------- * 5.72
1.2941 0.001

First I take care of my fractions:

0.5230/1.2941 = 0.4041⁴¹ (4 SFs retained)

73.152-2.35 = 70.80² (2 digits of precision retained)
70.80²/0.001 = 70802 (w/b 70000 for 1 SF)

Problem is now:

0.4041⁴¹ - 70000 ^(70802) * 5.72

Multiplication first:
70802 * 5.72 = 404987^.44 (0 digits of precision)

Then Subtraction:

0.4041⁴¹ - 404987^.44 = -404987.0359

-404987.0359 = -404987.04 (2 digits of precision)


I've tried submitting -404987.04 AND -404987 and both are incorrect. I can't figure it out! Ripping my hair out! Please help

Why would you submit -404987.04? That has 8 SF. You started with a maximum of 5 SF.
Why would you submit -404987? That has 6 SF. You started with maximum of 5 SF.
You seem to be confusing FIGURES with DIGITS to the right of the decimal point.
You may have mistaken one of your tiny '2's for a real '2'.

Please identify the number of significant figures in each value:

0.5230 -- (4 SF)
73.152 -- (5 SF)
2.35 -- (3 SF)
5.72 -- (3 SF)
1.2941 -- (5 SF)
0.001 <== Personally, I would consider this a Scaling Factor, and not anything else, unless I know something else about it. Example: 2.73 and 2.73E4 both have 3 Significant Figures.
4, 5, 3, 3, 5 -- You should end up with 3 Significant Figures

0.5230/1.2941 = 0.404141875 ==> 0.4041 (4)
73.152 - 2.35 = 70.802 ==> 70.8 (3)
70.8 / 0.001 = 70.8E-3 ==> 70,800 (3)
70,800 * 5.72 = 404,976 ==> 405,000 (3)
0.4041 - 405,000 = -404,999.959 ==> -405,000 (3)

Keep this in mind when adding values of substantially different magnitudes:

Mass of the Earth + One Grain of Sand = Mass of the Earth

Try another one and show us your clean and careful work.

 

[Dr.Peterson]

Here's how I'd do it; I'm not familiar with using superscripts as you did, which seems very confusing; I'll use a bar to separate "trusted" digits (those that are considered reliable based on significant figures or places) from others.

You want to evaluate 0.5230/1.2941 - (73.152 - 2.35)/0.001 * 5.72. It is possible that 0.001 is meant to be thought of as an exact number, so I'll take it that way after first evaluating it as having one significant figure:

0.5230/1.2941 - (73.152 - 2.35)/0.001 * 5.72 =
0.4041|41 - (70.80|2)/0.001 * 5.72 =
0.4041|41 - 7|0802 * 5.72 =
0.4041|41 - 4|04987.44 =
-4|04987.03

Keeping only the one trusted digit, the answer would be -400000!

If we take 0.001 as exact, we have

0.5230/1.2941 - (73.152 - 2.35)/0.001 * 5.72 =
0.4041|41 - (70.80|2)/0.001 * 5.72 =
0.4041|41 - 7080|2 * 5.72 =
0.4041|41 - 404|987.44 =
-404|987.03

so the answer would be -405000.

Subtraction between two numbers that differ so greatly in size essentially means that the smaller number can be ignored. In the second version here, only the thousands and higher places in the larger number are "trusted", to us my terms, so all digits in the smaller number are "down in the noise" and have no effect on the result.

In your answers, you included unreliable digits.

 

[themuffinyamber]

Here's how I'd do it; I'm not familiar with using superscripts as you did, which seems very confusing; I'll use a bar to separate "trusted" digits (those that are considered reliable based on significant figures or places) from others.

You want to evaluate 0.5230/1.2941 - (73.152 - 2.35)/0.001 * 5.72. It is possible that 0.001 is meant to be thought of as an exact number, so I'll take it that way after first evaluating it as having one significant figure:

0.5230/1.2941 - (73.152 - 2.35)/0.001 * 5.72 =
0.4041|41 - (70.80|2)/0.001 * 5.72 =
0.4041|41 - 7|0802 * 5.72 =
0.4041|41 - 4|04987.44 =
-4|04987.03

Keeping only the one trusted digit, the answer would be -400000!

If we take 0.001 as exact, we have

0.5230/1.2941 - (73.152 - 2.35)/0.001 * 5.72 =
0.4041|41 - (70.80|2)/0.001 * 5.72 =
0.4041|41 - 7080|2 * 5.72 =
0.4041|41 - 404|987.44 =
-404|987.03

so the answer would be -405000.

Subtraction between two numbers that differ so greatly in size essentially means that the smaller number can be ignored. In the second version here, only the thousands and higher places in the larger number are "trusted", to us my terms, so all digits in the smaller number are "down in the noise" and have no effect on the result.

In your answers, you included unreliable digits.

I forgot, I, too, tried -400,000 on one try! To no avail! Seeing your breakdown, -405000 seems to make the most sense to me of any attempt. However, I tried -405000 just now and it was also incorrect. I'm starting to think the answer key has an issue... Eek! So frustrating.

I like using | to differentiate from your significant figures, I think I will start to do that rather than the superscript. ​

I meet with this teacher tomorrow... I will update you both... Thank you for taking a whack at this problem with me, I do appreciate it. It's really making me scratch my head

 

[Dr.Peterson]

I forgot, I, too, tried -400,000 on one try! To no avail! Seeing your breakdown, -405000 seems to make the most sense to me of any attempt. However, I tried -405000 just now and it was also incorrect. I'm starting to think the answer key has an issue... Eek! So frustrating.

I like using | to differentiate from your significant figures, I think I will start to do that rather than the superscript. ​

I meet with this teacher tomorrow... I will update you both... Thank you for taking a whack at this problem with me, I do appreciate it. It's really making me scratch my head

I'll be interested in the result. I think you're saying that a computer program is telling you whether your answer is "correct", but never tells you what it considers correct (since a written answer key would). There can be significant ambiguity in problems like this, so we may both be missing something (and your teacher may not be sure, either!).

 

[tkhunny]

It's also important to note that not all numbers can be represented EXACTLY in computer systems. This makes it more difficult to programmatically calculate or compare two values. Generally, if it doesn't have an EXACT and FINITE binary representation, then it doesn't really exist in the computer system. There are ways around it and there are exceptions and there are accommodations, but it can be a touchy concept.

 

[themuffinyamber]

I'll be interested in the result. I think you're saying that a computer program is telling you whether your answer is "correct", but never tells you what it considers correct (since a written answer key would). There can be significant ambiguity in problems like this, so we may both be missing something (and your teacher may not be sure, either!).

OH MY GOODNESS. -400000 is the correct answer, however IT NEEDED TO BE IN SCIENTIFIC NOTATION. Kicking myself in the booty. Thank you all for your help!!:cool:

 

[Dr.Peterson]

OH MY GOODNESS. -400000 is the correct answer, however IT NEEDED TO BE IN SCIENTIFIC NOTATION. Kicking myself in the booty. Thank you all for your help!!:cool:

Yup. When I help students who are working on an online computer program, there are often instructions (like "enter a number in scientific notation") in small blue writing next to the answer blank. I've become accustomed to reminding them, "Don't forget to check the blue letters before you hit Enter!" But then I forget, too.

I sometimes wish everyone would include a screenshot of what they're doing along with their question.

 

[themuffinyamber]

Yup. When I help students who are working on an online computer program, there are often instructions (like "enter a number in scientific notation") in small blue writing next to the answer blank. I've become accustomed to reminding them, "Don't forget to check the blue letters before you hit Enter!" But then I forget, too.

I sometimes wish everyone would include a screenshot of what they're doing along with their question.

It actually didn't formally instruct me to do so, it apparently expects it any time a larger number is being entered as a general rule that I was not aware of. Learned the hard way! Lol!!

 

[mmm4444bot]

… When I help students who are working on an online computer program, there are often instructions (like "enter a number in scientific notation") in small blue writing next to the answer blank.

It actually didn't formally instruct me to do so …

This issue is a regular thorn in the side of students, at the campus where I work as a tutor.

Many introductory courses use software for doing homework, and the software doesn't say anything about number form or syntax requirements. More often than not, instructors do not provide this information, either. The software often rejects correct answers; sometimes, I cannot figure out what it wants.

Fortunately, technology in math classes seems to be getting better. I advise students to take a cell-phone image, and then raise the matter in class or during office hours.

 

[Dr.Peterson]

This issue is a regular thorn in the side of students, at the campus where I work as a tutor.

Many introductory courses use software for doing homework, and the software doesn't say anything about number form or syntax requirements. More often than not, instructors do not provide this information, either. The software often rejects correct answers; sometimes, I cannot figure out what it wants.

Fortunately, technology in math classes seems to be getting better. I advise students to take a cell-phone image, and then raise the matter in class or during office hours.

When I teach a course using such software, it provides a way to contact your instructor when you have questions. I tell the students that if they question its judgment of their answer, they can use that mechanism to show me the question and their answer; I can then either tell them that they are in fact wrong, or override their score if I consider it valid. This puts a human behind the computer.