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Math with Significant Digits addition

Rounding to a positive range of widespread digits, or to a named “location”, is reasonably straightforward. The actual query is available in the way of spherical solutions to the “appropriate” range of widespread digits. If you have been given a few values (lengths, say, or masses) and informed to paintings with them, arriving at a solution that’s rounded to the “appropriate” range of sig-digs, what does this mean?

The concept is this: Suppose you degree a block of timber. The duration is 5.6 inches, the width is 4.4 inches, and the thickness is 1.7 inches, as a minimum as first-rate you could inform out of your tape degree. To discover the quantity, you will multiply those 3 dimensions, to get 41.888 cubic inches.

But are you able to really, with a direct face, declare to have measured the quantity of that block of timber to the nearest thousandth of a cubic inch?!? Not hardly! Each of your measurements turned into correct (as a long way as you could inform) to 2 widespread digits: your tape degree turned into marked off in tenths of inches, and also you wrote down the nearest 10th of an inch that you can see. So you can’t declare 5 decimal locations of accuracy, due to the fact none of your measurements exceeded two digits of accuracy.

As a result, you could simplest declare two widespread digits for your solution to find in sig fig calculator. In different words, the “appropriate” range of widespread digits is two, and you will report (for your physics lab report, for instance) that the quantity of the block is 42 cubic inches, approximately.

How do you spherical after they provide you with a gaggle of numbers to add? You might add (or subtract) the numbers, as usual, however, then you definitely might spherical the solution to the identical decimal location as the least-correct range.

  • Round to the proper range of widespread digits:

13.214 + 234.6 + 7.0350 + 6.38

Looking at the numbers, I see that the second one range, 234.6, is the simplest correct to the tenths location; all of the different numbers are correct to a more range of decimal locations. So my solution will be rounded to the tenths location:

13.214 + 234.6 + 7.0350 + 6.38 = 261.2290

The digit withinside the tenths location is a 2, and it is accompanied through another 2, so I might not be rounding up. Rounding to the tenths location, I get:

13.214 + 234.6 + 7.0350 + 6.38 = 261.2

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