MathematicsExam code: 0580
Rounding, Estimation and Bounds
Number
Finding the first significant figure
- Reading left to right, the first significant figure is the first non-zero digit
- In 5081 it is the 5
- In 0.00407 it is the 4
- Zeros in front of that digit only position the number and are never significant
- Zeros sitting between non-zero digits are significant, because they carry information
- The second significant figure of 5081 is the 0
Rounding and padding
- Count rightwards to the required figure, then apply the usual rounding rule
- Large numbers are padded with zeros out to the decimal point
- 5081 to two significant figures is 5100
- For a decimal, zeros fill the gap from the point up to where the significant figures begin
- 0.00407 to two significant figures is 0.0041
Exam tip
Three significant figures unless told otherwise
On the calculator paper, an answer that is not exact goes to 3 significant figures, and an angle in degrees to 1 decimal place, whenever the question names no accuracy of its own; an exact answer stays in full. The schemes print such answers to 3 significant figures or longer, as in 4.27 or 4.268…, so a shorter 4.3 misses the final mark. The non-calculator paper sets no such default.
Worked example
Rounding to significant figures
Write 0.004 078 2 to 3 significant figures, and 46 851 to 2 significant figures.
Solution:
- The first significant figure is the first non-zero digit, so leading zeros never count
- In 0.004 078 2 the first significant figure is the 4, the second is the 0 after it, and the third is the 7
- The next digit is 8, which is 5 or more, so the 7 rounds up to 8
- 0.004 078 2 = 0.004 08 to 3 significant figures
- In 46 851 the first two significant figures are 4 and 6
- The next digit is 8, so the 6 rounds up to 7
- The place holders must stay, so the answer is 47 000, not 47