Question #85a3f

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Answer 1 · 2017-03-31T16:39:34

Do not round off to the correct number of significant figures until the final calculation.

If you round off after each step, you may get accumulated round-off error.

Always carry at least one extra digit (called a guard digit) to prevent round-off error.

Any intermediate answers that you must report for grading should be rounded off to the correct number of significant figures.

If you must use an intermediate answer in a later calculation, use its unrounded value (not the rounded value that you reported earlier).

Example

(a) Rounding off at each step

Calculate the value of $2.350(4.0+6.361)$ .

$4.0 + 6.311 = 10.4$ (3 significant figures)

$2.350 × 10.4 = 24.4$ (3 significant figures)

(b) Carrying a guard digit

Calculate the value of $2.350(4.0+6.361)$ .

$4.0 + 6.361 = 10.36$ (1 decimal place + 1 guard digit)

$2.350 × 10.36 = 24.36$ (3 significant figures + 1 guard digit)
$= 24.3$ (3 significant figures)

If you retain all the digits in your calculator, the answer becomes $"24.348 35"$ which, on rounding, becomes $24.3$ .

Moral: Retain one guard digit and round off only at the end.