Decimal Places & Significant Figures Round Off
In this lesson, we first begin by covering the Cambridge standards for rounding intermediate and final answers. Next, students will learn the methods for rounding by decimal places and by significant figures.
Finally, we will cover a special round off exception, focusing on how to round the number 9.9995.
Related Lessons:
Cambridge GCE O Level Round Off Standard
In accordance with GCE O Level Syllabus, unless a different level of accuracy is specified in the question:
- non-exact numerical answers must be correct to 3 significant figures
- non-exact numerical answers in degree must be round to 1 decimal place
- intermediate answers must round to at least 4 significant figures
Rounding Off By Decimal Places
When rounding by decimal numbers, observe the following key rules:
- All non-zero digits are significant.
- Zeros between non-zero digits are significant.
- If the next digit is 5 or more, round up; if it is less than 5, keep the digit the same.
- 65.456 = 65.46 (2 d.p.)
- 65.451 = 65.45 (2 d.p.)
- Trailing zeros may be significant
- 2.4950 = 2.50 (2 d.p. – note that the ending zero is significant)
Rounding Off By Significant Figures
When rounding by significant figures, observe the following key rules:
- All non-zero digits are significant.
Zeros between non-zero digits are significant. - If the next digit is 5 or more, round up; if it is less than 5, keep the digit the same.
- 8436 = 8000 (1 s.f.)
- 8436 = 8400 (2 s.f)
- 8436 = 8440 (3 s.f.)
- All leading zeros are not significant
- 0.000312 = 0.00031 (2 s.f. by counting the first non-zero from the left)
- Trailing zeros may be significant (i.e. counted)
- 2.4695 = 2.470 (4 s.f. – note that the last zero is significant)
Rounding Exceptions: How to Handle Special Cases
What happens when we need to round a special number such as 9.9995 to 3 decimal places or 3 significant figures?
In this case, the digit being rounded causes a carry-over across several digits. Since the next digit is 5, we round up. Adding 1 to the last retained digit changes 9.999 into 10.000, increasing the value of the number. So we may need to reduce the value of the number.
Hence, the rounded results are:
- 10.000 (3 d.p.)
- 10.0 (3 s.f.).
Similarly, if the number is rounded to 2 decimal places or significant figures, the answers are:
- 10.00 (2d.p.)
- 10 (2s.f.)
Watch Full Concept Breakdown
Below is the video that explains, step by step, the concepts covered above on rounding to decimal places, significant figures, and special cases of rounding off. Students are encouraged to go through the video, as it provides clearer insight and deepen students’ understanding of the concepts.