Significant Figures homework help

[carlodelmundo]

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?

 

[mg0stisha]

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).

 

[carlodelmundo]

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?

 

[mg0stisha]

Because in this case it's not about the rounding rules, but it's about precision!

 

[carlodelmundo]

Since the least precise number is 100 (1 significant figure) we automatically change 10.5 to 10?

What's the "rule" to addition/subtraction?

 

[mg0stisha]

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?

 

[carlodelmundo]

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

 

[mg0stisha]

Both correct (after the edit on the second one!) Nice work :)