Rounding Off Uncertain Digits

Rounding Off Uncertain Digits

When a computation produces a number with more digits than justified, you must round it off. The rules are:

• If the digit to be dropped is more than 5, raise the preceding digit by 1.
  • 2.746 rounded to three significant figures → 2.75
• If the digit to be dropped is less than 5, leave the preceding digit unchanged.
  • 1.743 rounded to three significant figures → 1.74
• If the digit to be dropped is exactly 5, look at the preceding digit:
  • If the preceding digit is even, simply drop the 5.
  • If the preceding digit is odd, raise it by 1.

Examples with the 5 rule:

• 2.745 rounded to three significant figures → 2.74 (preceding digit 4 is even)
• 2.735 rounded to three significant figures → 2.74 (preceding digit 3 is odd)

Rounding in Multi-Step Calculations

In complex calculations, retain one extra digit beyond the significant figures in intermediate steps. Round off only at the end. This prevents rounding errors from building up.

Example: The reciprocal of 9.58 (three significant figures) is 0.1044 if you keep one extra digit. Rounding 0.1044 to three significant figures gives 0.104. Now take the reciprocal of 0.104: 1/0.104 = 9.62 (three significant figures). But the original value was 9.58 — we have introduced an error.

If instead we had kept the intermediate result as 0.1044 and then taken the reciprocal to three significant figures: 1/0.1044 = 9.58. We retrieve the original value. …