# Significant Figures

- All non-zero digits are significant.

42.3 has three significant figures.

243.4 has four significant figures.

24.123 has five significant figures.

- A zero becomes significant figure if it appears between two non-zero digits.

5.03 has three significant figures.

5.604 has four significant figures.

4.004 has four significant figures.

- Leading zeros or zeros placed to the left of the number are never significant.

0.543 has three significant figures.

0.045 has two significant figures.

0.006 has one significant figure.

- Trailing zeros or zeros placed to the right of the number are significant.

4.330 has four significant figures.

433.00 has five significant figures.

343.000 has six significant figures.

- In exponential notation, the numerical portion gives the number of significant figures.

1.32 Ã— 10^{â€“2} has three significant figures.

1.32 Ã— 10^{4} has three significant figures.

# Rules for arithmetic operations with significant figures

**Rule I**

In addition or subtraction, the final result should retain as many decimal places are there are in the number with the least decimal places.

**Rule II**

In multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures.

# Rounding off uncertain digits

The preceding digit is raised by 1 if the insignificant digit to be removed is more than 5 and is left unchanged if the later is less than 5.

When the insignificant digit to be removed is 5 and the uncertain digit is even, 5 is simply dropped, and if it is odd, then the preceding digit is raised by 1.