Question

The number of significant figures in \(1.20 \times 10^{2}\) is (a) 3 (b) 2 (c) 5 (d) 4

Short answer

The number of significant figures in \(1.20 \times 10^{2}\) is 3.

Step-by-step solution

Defining the Number

First, identify the number. In this case, the number is \(1.20 \times 10^{2}\).

Recognizing the significant figures

Consider the part of the number before the multiplication sign as \(\(a\)\) (in notation \(a \times 10^{n}\)). Here \(a = 1.20\). Count the number of digits in \(a\). Zeroes appearing between other digits, such as the zero between 1 and 2 are considered significant.

Counting the Significant Figures

We can count the digits in \(a\), i.e., how many digits in '1.20'. We see that there are three digits.

Conclusion

So, the number of significant figures in \(1.20 \times 10^{2}\) is 3, which is the count of digits in \(a\).

Key concepts

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is commonly used in chemistry and physics to deal with atomic scales and astronomical distances. For example, the mass of a proton is approximately \( 1.67 \times 10^{-27} \) kilograms, which is much more compact than writing out all 27 zeros.

When writing a number in scientific notation, only the significant figures are represented before the multiplication sign, which means that \(1.20 \times 10^{2} \) effectively contains three significant digits. The exponent part, \(10^{2}\), merely indicates the order of magnitude or how many places the decimal point is moved. Remember, the exponent itself does not contribute to the number of significant figures.

Precision in Measurement

Precision in measurement refers to how closely individual measurements agree with each other, often linked to the concept of significant figures in chemistry education. These figures provide a clear hint about the precision of the reported data. It's important to recognize that not all digits in a number carry the same weight in precision. For instance, trailing zeroes to the right of the decimal point are significant because they imply that measurement was precise enough to reach that degree of accuracy.

In the number \(1.20\), each digit is significant: the '1' and '2' are non-zero digits and always count, while the '0' is significant because it comes after a decimal point and after a non-zero digit. This pinpoints the measurement down to the hundredths place, indicating a high level of precision.

Chemistry Education

Chemistry education often involves gauging the composition and properties of substances, where accuracy and precision are paramount. Understanding significant figures is fundamental in this field as it facilitates error analysis and helps in reporting results in a standardized way. In classroom settings, chemistry students are taught to use significant figures to reflect the reliability of their experimental data.

By recognizing that \(1.20 \times 10^{2}\) has three significant figures, a student acknowledges the scale of precision determined during the measurement process. This precision communicates to others in the field the confidence level of the measurement, which is essential for experiments, scientific calculations, and when comparing results with those of others. Mastering the use of significant figures, alongside scientific notation, prepares students for advanced scientific studies and research that demand meticulous attention to measurement details.