Why does 6.8347 round to 6.83 for three sig figs?

Six point eight three is the number you get when you round six point eight three four seven to three significant figures because you keep the first three nonzero digits and the next digit is less than five so you do not increase the last kept digit.

Rounding to three significant figures means you look at the first three digits that matter and then decide whether to change the last one based on the next digit, and here the first three digits are six point eight three and the fourth digit is four which is less than five so you leave the third digit as it is; think of it like trimming a pencil to a shorter length where you look at the piece you are cutting off and if it is small you do not add to the main piece, and since the digit after the third significant figure is smaller than five you do not round up; use place value to keep track by writing the number as six point eight three four seven and underline the third significant figure, then check the next digit which tells you whether to increase the underlined digit or keep it the same.

A common mistake is thinking you always round by looking at the last digit of the original number instead of the digit immediately after the final significant figure, and a quick fix is to mark the third significant digit with a pencil dot before checking the next digit; another misconception is confusing significant figures with decimal places, and the solution is to remember significant figures count all meaningful digits starting from the first nonzero, not just digits after the decimal; some students forget that zeros between nonzero digits are significant, so write numbers clearly and count from the first nonzero digit to avoid errors.

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Rounding 6.8347 to 3 Significant Figures

1. Look at first three significant digits
2. Check the next digit after them
3. If next digit < 5, do not increase
4. Write number and underline third digit
5. Use place value to track digits

Common Rounding Mistakes for 3 Sig Figs

1. Looking at the last original digit
2. Confusing significant figures with decimal places
3. Forgetting zeros between nonzero digits are significant

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