Understanding the Concept of Significant Figures in Measurement- What They Represent and How to Use Them

What is meant by significant figures of a measurement?

Significant figures, also known as significant digits, are the digits in a number that carry meaning in terms of precision or accuracy. They are an essential part of scientific notation and are used to indicate the level of confidence we can have in a measurement. Understanding significant figures is crucial for scientists, engineers, and anyone else working with numbers, as it helps to communicate the reliability of their findings and calculations. In this article, we will explore the concept of significant figures, their importance, and how to determine them in different scenarios.

In the simplest terms, significant figures are the digits that are known with certainty, plus one uncertain digit. For example, if we measure the length of an object and get a value of 3.45 cm, we can be confident that the first three digits (3, 4, and 5) are accurate, but the last digit (5) is an estimate. This means that the measurement has three significant figures.

Rules for determining significant figures

There are several rules to follow when determining the number of significant figures in a measurement:

1. All non-zero digits are significant. For instance, in the number 123, all three digits are significant.
2. Zeros between non-zero digits are also significant. For example, in the number 1001, all four digits are significant.
3. Leading zeros (zeros to the left of the first non-zero digit) are not significant. In the number 0.00345, only the digits 3, 4, 5, and the trailing zero are significant.
4. Trailing zeros in a number with a decimal point are significant. For instance, in the number 1.230, all five digits are significant.
5. In scientific notation, all digits are significant. For example, in the number 1.23 × 10^4, all three digits are significant.

Significant figures in calculations

When performing calculations with measurements that have significant figures, it is important to maintain the proper number of significant figures in the final answer. This is done by following the rules of significant figures in arithmetic operations:

1. Addition and subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.
2. Multiplication and division: The result should have the same number of significant figures as the measurement with the fewest significant figures.

For example, if we have the following measurements:

– 3.45 cm (3 significant figures)
– 2.1 cm (2 significant figures)
– 0.050 m (3 significant figures)

When adding these measurements, the result should have 2 decimal places (since 2.1 cm has the fewest decimal places):

3.45 cm + 2.1 cm = 5.55 cm

However, when multiplying or dividing these measurements, the result should have 2 significant figures (since 2.1 cm has the fewest significant figures):

3.45 cm × 2.1 cm = 7.215 cm² (rounded to 2 significant figures: 7.2 cm²)
0.050 m ÷ 3.45 cm = 0.01449 m (rounded to 2 significant figures: 0.014 m)

In conclusion, understanding what is meant by significant figures of a measurement is crucial for accurately representing the precision and reliability of scientific data. By following the rules for determining significant figures and maintaining the proper number of significant figures in calculations, scientists and engineers can communicate their findings with confidence and ensure the accuracy of their work.