Significant Figures homework help

In summary, the significant figures rule is to round numbers down to the nearest whole number when there is a lack of precision after the decimal point.
  • #1
carlodelmundo
133
0

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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  • #2
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).
 
  • #3
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?
 
  • #4
Because in this case it's not about the rounding rules, but it's about precision!
 
  • #5
Since the least precise number is 100 (1 significant figure) we automatically change 10.5 to 10?

What's the "rule" to addition/subtraction?
 
  • #6
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?
 
  • #7
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:
  • #8
Both correct (after the edit on the second one!) Nice work :)
 

1. What are significant figures and why are they important in science?

Significant figures, also known as significant digits, are the meaningful and accurate digits in a measurement or calculation. They are important in science because they represent the precision and accuracy of a measurement or calculation. In other words, significant figures help to convey the level of confidence in a result and ensure that data is reported correctly.

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

To determine the number of significant figures in a number, follow these rules:

  • Non-zero digits are always significant.
  • Zeroes between non-zero digits are significant.
  • Zeroes at the beginning of a number are never significant.
  • Zeroes at the end of a number are significant if there is a decimal point present.
  • Zeroes at the end of a number are not significant if there is no decimal point present.

3. How do I perform calculations with significant figures?

When performing calculations with significant figures, the result should be rounded to the same number of significant figures as the measurement with the least number of significant figures. For addition and subtraction, the result should have the same number of decimal places as the measurement with the least number of decimal places. For multiplication and division, the result should have the same number of significant figures as the measurement with the least number of significant figures.

4. Can I ever add or subtract numbers with different numbers of significant figures?

Yes, you can add or subtract numbers with different numbers of significant figures as long as you round the final result to the correct number of significant figures. This ensures that the result is not more precise than the original measurements.

5. How do I use significant figures in scientific notation?

In scientific notation, the number before the "x10" represents the significand and should include all significant figures. The exponent after the "x10" represents the number of decimal places and should not be counted as a significant figure. When multiplying or dividing numbers in scientific notation, use the same rules for significant figures as mentioned in question 3.

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