Circle In Degree & Radian
In this lesson, you will learn how angles in a circle can be measured using both degrees and radians. You will understand that a full circle is 360° or 2π radians, and learn how to convert between these two units.
Related Lessons:
Convert Between Degree & Radian
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)
Arc Length & Area Formula For Circle
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)
Example 1
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.)
Example 2
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.)
Example 3
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.)
Example 4
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.)