I’m confused as to how, when and why I’m supposed to use significant digits vs when to carry all the decimals my calculator spits out. This is for surveying/civil engineering related fields in particular. My professor has covered both topics extensively but didn’t do a very good job explaining when said rules apply.
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Always carry the full values of your calculator when doing all operations. Rounding to a certain number of sig figs is a last-step action once you have the answer you’re looking for. The point of sig figs is to show to others how confident you are in the accuracy of a *final answer* you are giving, not of every intermediary step of your process.
If you have a notebook full of calculations for a specific engineering problem, think of enclosing that notebook in a black box, where only the measurements you put in and the start and the final answer are visible. This black box is essentially asking the question, “If I put in XYZ values, what is the answer?” What happens inside the black box, as far as finding the un-rounded answer goes, does not matter.
Once you get an un-rounded answer, you analyze the way you combined XYZ inside your black box to determine how many sig figs your answer should have, and you clip your final answer based on that. This is what sig figs rules are for, they take all of the loss of precision of your black box and wrap it into a simple operation you can apply at the very end to safely account for all of it.
Always carry the full values of your calculator when doing all operations. Rounding to a certain number of sig figs is a last-step action once you have the answer you’re looking for. The point of sig figs is to show to others how confident you are in the accuracy of a *final answer* you are giving, not of every intermediary step of your process.
If you have a notebook full of calculations for a specific engineering problem, think of enclosing that notebook in a black box, where only the measurements you put in and the start and the final answer are visible. This black box is essentially asking the question, “If I put in XYZ values, what is the answer?” What happens inside the black box, as far as finding the un-rounded answer goes, does not matter.
Once you get an un-rounded answer, you analyze the way you combined XYZ inside your black box to determine how many sig figs your answer should have, and you clip your final answer based on that. This is what sig figs rules are for, they take all of the loss of precision of your black box and wrap it into a simple operation you can apply at the very end to safely account for all of it.
In chemistry, the rules of Sig Figs are as follows: when adding or subtracting you keep all available decimal places. When multiplying and dividing, your answer should have the same number of Sig figs as your term with the lowest number of Sig figs (ie 0.35*0.6385868538855 should only have two sig figs). Lastly, one should only express decimal places beyond the appropriate number of sig figs in the final answer, and not in intermediate steps along the way. Each intermediate step of your calculations should carry all decimals through until the final answer is reached, and only trim down sig figs at the end. This keeps the precision of the final answer within the precision tolerance of the measurement devices used.
In chemistry, the rules of Sig Figs are as follows: when adding or subtracting you keep all available decimal places. When multiplying and dividing, your answer should have the same number of Sig figs as your term with the lowest number of Sig figs (ie 0.35*0.6385868538855 should only have two sig figs). Lastly, one should only express decimal places beyond the appropriate number of sig figs in the final answer, and not in intermediate steps along the way. Each intermediate step of your calculations should carry all decimals through until the final answer is reached, and only trim down sig figs at the end. This keeps the precision of the final answer within the precision tolerance of the measurement devices used.
Always carry the full values of your calculator when doing all operations. Rounding to a certain number of sig figs is a last-step action once you have the answer you’re looking for. The point of sig figs is to show to others how confident you are in the accuracy of a *final answer* you are giving, not of every intermediary step of your process.
If you have a notebook full of calculations for a specific engineering problem, think of enclosing that notebook in a black box, where only the measurements you put in and the start and the final answer are visible. This black box is essentially asking the question, “If I put in XYZ values, what is the answer?” What happens inside the black box, as far as finding the un-rounded answer goes, does not matter.
Once you get an un-rounded answer, you analyze the way you combined XYZ inside your black box to determine how many sig figs your answer should have, and you clip your final answer based on that. This is what sig figs rules are for, they take all of the loss of precision of your black box and wrap it into a simple operation you can apply at the very end to safely account for all of it.
In chemistry, the rules of Sig Figs are as follows: when adding or subtracting you keep all available decimal places. When multiplying and dividing, your answer should have the same number of Sig figs as your term with the lowest number of Sig figs (ie 0.35*0.6385868538855 should only have two sig figs). Lastly, one should only express decimal places beyond the appropriate number of sig figs in the final answer, and not in intermediate steps along the way. Each intermediate step of your calculations should carry all decimals through until the final answer is reached, and only trim down sig figs at the end. This keeps the precision of the final answer within the precision tolerance of the measurement devices used.
You use all the decimal places the calculator gives you while you’re doing the calculation. You only round to however many significant figures when you’re giving your final answer. You want the most accurate answer possible, and rounding too early can change your answer.
You use all the decimal places the calculator gives you while you’re doing the calculation. You only round to however many significant figures when you’re giving your final answer. You want the most accurate answer possible, and rounding too early can change your answer.
You use all the decimal places the calculator gives you while you’re doing the calculation. You only round to however many significant figures when you’re giving your final answer. You want the most accurate answer possible, and rounding too early can change your answer.
Let’s say I want the sqrt(2.00)^2
I know the answer should be 2.00, but if I round too soon I get an issue
Sqrt(2.00) = 1.41
1.41^2 = 1.99
1.99 is not 2.00, so clearly something went wrong. I rounded too soon.
Always round once you’ve finished calculating, but if you need to calculate further, you need to use the exact value you calculated.
Sqrt(2.00) is indeed 1.41 and 1.41^2 is indeed 1.99, but sqrt(2.00)^2 = 2.00
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