Physics is a human effort to study the natural world and to understand how the universe behaves. Therefore any theory (no matter how interesting it looks) is useless unless it is supported by experimental evidence. Doing an experiment usually involves making quantitative measurements. However, in order for the measured values (or data) to be meaningful, it is very important to understand the limitations of the instruments used and to recognize the possible sources of error.
Assume that you want to calculate the surface area and volume of your physics textbook. Of course, you need to measure the book's dimensions (length, width and thickness). Using a ruler, you first measure the length of the textbook. Since the smallest division on the ruler is the millimetre, you can only give an upper limit ($26.3\,\text{cm}$) and a lower limit ($26.1\,\text{cm}$) for the length. Due to the limitations of the instrument (the ruler in this case) you can then say that the correct length ($L$) of the textbook is most probably between these two values. This value is written as ($L = 26.2 \pm 0.1$ cm), where the first number is called the measured value and the second number is called the uncertainty (or error) in the measurement. Similarly, you measure the width ($W$) and the thickness ($T$) of the textbook to be ($W = 20.6 \pm 0.1$ cm) and ($T = 3.9 \pm 0.1$ cm) respectively. In these measurements, the first digit after the decimal point is uncertain, making it meaningless (or insignificant) to include more digits. The digits in a measured value, up to and including the first uncertain digit, are called significant figures. So, there are three significant figures in $L$ and $W$ and two significant figures in $T$. Note that we cannot write the length as $L = 26.20$ cm, since it will then include two uncertain digits.
In counting the number of significant figures in a measurement, we start from the first non-zero digit and end at the first uncertain digit. If the uncertainty of a measurement is known, then it becomes easy to specify the uncertain digit and count the number of significant figures. However, if the uncertainty of a measured value is not known, then we need to be careful. If there is no decimal point in the number, the last non-zero digit is considered to be the first uncertain digit. If the number contains a decimal point, the last digit after the decimal (whether it is a zero or not) is considered uncertain. Ambiguity in the number of significant figures is avoided by using the scientific notation, in which only one digit is kept to the left of the decimal point, while the remaining digits, up to and including the uncertain one, are moved to the right. Of course, we must multiply by the appropriate exponent. See Table 0.1 for examples.
| Measured Value | Scientific Notation | Number of Significant Figures |
| $9.80$ | $9.80$ | 3 |
| $120$ | $1.2 \times 10^2$ | 2 |
| $120 \pm 2$ | $(1.20 \pm 0.02 ) \times 10^2$ | 3 |
| $120.0$ | $1.200 \times 10^2$ | 4 |
| $1.00560$ | $1.00560$ | 6 |
| $0.00560$ | $5.60 \times 10^{-3}$ | 3 |
| $375 \times 10^{-9}$ | $3.75 \times 10^{-7}$ | 3 |