Why Does the Answer Key Give 188.1 for This Significant Figures Calculation?

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SUMMARY

The calculation of the expression (2.526/3.1) + (0.470/0.623) + (80.705/0.4326) results in a final value of 188.1192 when computed without premature rounding. The discrepancy with the answer key, which states the result is 188.1, arises from the incorrect application of significant figures during intermediate steps. The correct approach is to maintain precision throughout the calculation and only round the final result to the appropriate number of significant figures, which in this case should yield 188.1 when rounded correctly.

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Homework Statement



Add the following:

(2.526/3.1) + (0.470/0.623) + (80.705/0.4326)


2. The attempt at a solution

= (2.526/3.1) + (0.470/0.623) + (80.705/0.4326)
= (0.81) + (0.754) + (186.6)
= 188.2

I have calculated the answer (using sig figs) to be 188.2, however, the answer key says it is 188.1.
 
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Don't round off until the last step.
 
Doc Al said:
Don't round off until the last step.

= (2.526/3.1) + (0.470/0.623) + (80.705/0.4326)
= (0.8148) + (0.7544) + (186.55)
= 188.1192

If I don't apply sig figs to each step, then how would I know how many sig figs there would be in the final answer?
 
You can know how many sig figs in each step and still not round off until the end.
 
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Doc Al said:
You can know how many sig figs in each step and still not round off until the end.

Ok. I see. Thank you.
 

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