Tipler/Mosca significant figures

[walking]

In tipler and mosca it says that the number of significant figures in the result of addition or subtraction is no greater than the least number of significant figures beyond the decimal place of any of the numbers.

They give the example of 1.040+0.21342. Clearly, 1.040 has three significant figures beyond the decimal place whereas 0.21342 has five. So the result can only have a maximum of three significant figures beyond the decimal place. Hence 1.040+0.21342=1.253.

I have two questions:
1. Is "number of significant figures after the decimal point" simply another way of saying "decimal places"? (So would it be correct in the above example to say "1.253 (3 d.p)"?)
2. When we try to apply the rule to 2.34\cdot 10^2+4.93, is the answer 238.93 or 2.39*10^2, and why?

 

[kuruman]

If you express

2. When we try to apply the rule to $2.34\cdot 10^2+4.93$, is the answer 238.93 or 2.39*10^2, and why?

What rule are you applying? Note that the number of significant figures implied by the addition is 3 (what's to the left of the decimal counts) so 238.93 has 5 sig figs and is incorrect while 2.39×10² has 3 sig figs and is correct. For more on this go to
https://en.wikipedia.org/wiki/Significant_figures

 

[walking]

If you express

What rule are you applying? Note that the number of significant figures implied by the addition is 3 (what's to the left of the decimal counts) so 238.93 has 5 sig figs and is incorrect while 2.39×10² has 3 sig figs and is correct. For more on this go to
https://en.wikipedia.org/wiki/Significant_figures

I am applying the rule I mentioned at the start of my post. Tipler and Mosca say that there are two separate rules, one for multiplication and division of numbers, the other for addition and subtraction. The rule you are telling me is the one they say should be applied to multiplication and division, not addition and subtraction. Thus, I think your answer is wrong.

 

[jbriggs444]

2. When we try to apply the rule to 2.34\cdot 10^2+4.93, is the answer 238.93 or 2.39*10^2, and why?

If you want to make it a procedure using scientific notation, you could do this:

1. Convert one of the two numbers to share the same decimal exponent as the other. So either $$2.34\cdot 10^2 + 0.0493 \cdot 10^2$$ or $$234\cdot 10^0 + 4.93\cdot 10^0$$
2. Perform the addition.
3. Round off to remove any result digits where either addend has become insignificant. Either way, the "93" in the sum is insignificant and is rounded away.

This procedure agrees with what @kuruman is saying.

Note: If you are doing a multi-step calculation, you would not round off after each operation. Instead, you would keep track of the significant figures at each step along the way, noting which digits are significant or insignificant. You would keep full accuracy throughout the calculation and round only for the final reported result.