# Question 85a3f

Mar 31, 2017

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

#### Explanation:

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 $2.350 \left(4.0 + 6.361\right)$.

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

2.350 × 10.4 = 24.4 (3 significant figures)

(b) Carrying a guard digit

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

$4.0 + 6.361 = 10.36$ (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 $\text{24.348 35}$ which, on rounding, becomes $24.3$.

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