Sig fig question?

how do you add or minus numbers when it is a sig fig question? Show me an example and explanation such as


500-3.4564


577.88-34.4564


565765.9999-456.456456


500-3.0





and times and divide


55.745* 456.456


546.456/ 456.46


500/345.75


ty

Sig fig question?
Addition/Subtraction = Give final answer to the decimal place of the least precise value.





Examples:


500-3.4564


= 497





577.88-34.4564


= 543.42





565765.9999-456.456456


= 565309.5434





500-3.0


= 497





If you wanted a better example:


58.747 -1.2


= 57.5


Notice that 1.2 has 2 significant digits and 58.747 has 5 significant digits. However, in addition subtraction, you aren't concerned over significant digits, you are concerned over the least precise decimal place. In 1.2, the decimal place is the tenths place. Therefor you give your answer to the tenths place. This is why the final answer has 3 signifcant digits instead of 2.





Multiplication/Division = Give final answer to the significant figures of the value with the least significant figures





Examples:


55.745* 456.456


= 25445





546.456/ 456.46


= 1.1974





500/345.75


= 1.45
Reply:For addition or subtraction, your answer cannot have an accuracy more than the least accurate given. For example in the first question, 500 is good to the tens whereas 3.4564 is good to the ten-thousandths. So, you cannot expect your answer to be accurate to the ten-thousandths. Also, align the givens so that the decimal points are in line. Thus,


The answer is simply 500 - 3 = 497.





Correspondingly, the answer to the second one is


577.88


- 34.46 ( using rounding rules)


-----------


543.42





565765.9999


- 456.4565


---------------------


565309.5434





500


- 3


------


497





In multiplication and division, your answer cannot have more significant digits that the least significant number. This requires you know how to count sig figs. In the first one, the least number has 5 sig figs vs. 6, so your answer will have 5 sig figs.


Multiply the numbers as is and then limit the digits of the answer to the 5 sig figs. You get 25445.139 which has 8 sig figs. You reduce this to 5 to give final answer of 25445 only.





The answers to the rest of the division problems are: 1.1972 and 1.45





This requires also rounding off rules.





Hope this helps.





Is "ty", thank you? In that case, "ur welcom"
Reply:First, keep all numbers until the very end. Then assume that any missing decimal places are filled with a zero.





In the first example, 500.0000 - 3.4564 is 496.5436.





Finally, determine how many of the numbers to keep and round off to that number. The first case is a bit tricky because you must assume three sig figs in the answer, so the "keeper" for the answer is 497. As it turns out, it is the same answer as the last subtraction problem.





In multiply/divide, again keep all numbers then round off. For example, the third problem will have only three sig figs as the answer.