Significant Figures homework help

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Discussion Overview

The discussion revolves around the application of significant figures in a homework problem involving division and addition. Participants explore the rules governing significant figures and precision, particularly in the context of rounding and how it affects the final answer.

Discussion Character

  • Homework-related
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant states that when adding 100 and 10.5, the 10.5 should be rounded to 11 due to the precision of 100, leading to a denominator of 111.
  • Another participant argues that 10.5 should be rounded to 10 instead, as 100 is only precise to the hundreds place, resulting in an answer of 500 after rounding.
  • A question is raised about the rounding process, specifically why 10.5 rounds down to 10 rather than up to 11.
  • Participants discuss the distinction between significant figures and precision, noting that significant figures apply to multiplication and division, while precision applies to addition and subtraction.
  • One participant provides examples to illustrate how to determine significant figures and precision in different mathematical operations.
  • Another participant confirms their understanding of the rules after working through an example, concluding that the final answer should be 18 based on the precision of the numbers involved.

Areas of Agreement / Disagreement

Participants express differing views on how to round the number 10.5 in the context of the problem, indicating a lack of consensus on the application of rounding rules. The discussion remains unresolved regarding the correct approach to significant figures in this scenario.

Contextual Notes

Participants highlight limitations in understanding the rules of significant figures and precision, particularly in how they apply to different mathematical operations. There is also a mention of the need to accommodate the precision of the least precise number in calculations.

carlodelmundo
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Homework Statement



(5.25 * 104) / (100 + 10.5)

Homework Equations



Significant Figures Rule

The Attempt at a Solution



The answer in the book states 500 (which has 1 or 2 significant figures). In my first step, I did the addition first in the denominator (100 + 10.5). Adhering to our addition rules, I rounded 10.5 to 11 because 100 is the least precise (no decimal point precision). So the denominator I put was 111 (100 + 11). When I divide 5.25 * 104 / 111... I get 472.9729729 ... a repeating integer.

I left my answer as 473. But the answer is 500 according to the book. Can anyone show me why?
 
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I'm pretty sure you have to round the 10.5 to 10 (1 significant digit). The 100 is only precise to the hundreds place, and since 10 can't be precise to the hundreds place, 10 will have to do. From then on you'll only have 1 significant digit, giving you your answer of 500 (rounded up from 473).
 
How is this possible if the first digit after the decimal point is 5? Why do we round down to 10 and not to 11?
 
Because in this case it's not about the rounding rules, but it's about precision!
 
Since the least precise number is 100 (1 significant figure) we automatically change 10.5 to 10?

What's the "rule" to addition/subtraction?
 
Significant Figures and Precision are different entities. Significant Digits is used with multiplication and division, where as Precision is used with addition and subtraction.

For example, how many significant digits would 158 x 18.53 have?

For another example, to what precision would 11 + 6.9845 have?
 
1.) 3 digits (the 158 has 3 sig figs and has the least amount of sig figs)

2.) 11 + 6.9845 would have precision to 2 significant digits.

For #2, I think we add them holistically first, right? (11 + 6.9845 = 17.9845) then since we are precise to 2 sig figs... we just do 18? (or is it 17?)

[EDIT]

I understand now. Since 11 has no digits after the decimal point (no precision to the tenths place) we must truncate the answer to accommodate NO precision after the decimal. The answer is 18
 
Last edited:
Both correct (after the edit on the second one!) Nice work :)
 

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