Identifying Measurements with Four Significant Figures- A Comprehensive Guide

Which of the measurements contain four significant figures is a common question in scientific and engineering fields. Significant figures, also known as significant digits, are a way to express the precision of a measurement. Understanding how to identify and count significant figures is crucial for accurate data analysis and communication in these disciplines.

In the context of significant figures, a number is considered to have four significant figures if it contains four digits that are known with certainty, plus one estimated digit. This means that the first four digits are considered to be accurate, while the fifth digit is an approximation. To determine which measurements contain four significant figures, we need to examine each number carefully.

For example, let’s consider the following measurements:

1. 123.4 mg
2. 0.001234 g
3. 1.234 × 10^3 kg
4. 123.45 mL

To identify the number of significant figures in each measurement, we must follow the rules for determining significant figures:

1. All non-zero digits are significant.
2. Zeros between non-zero digits are significant.
3. Leading zeros (zeros before the first non-zero digit) are not significant.
4. Trailing zeros (zeros after the last non-zero digit) are significant if there is a decimal point present.

Applying these rules to the measurements above, we can determine the number of significant figures:

1. 123.4 mg has four significant figures (123 and 4 are non-zero, and the trailing zero is significant because there is a decimal point).
2. 0.001234 g has five significant figures (all non-zero digits are significant).
3. 1.234 × 10^3 kg has four significant figures (1, 2, 3, and 4 are non-zero, and the trailing zero is significant because there is a decimal point).
4. 123.45 mL has five significant figures (all non-zero digits are significant).

In conclusion, the measurements that contain four significant figures are 123.4 mg and 1.234 × 10^3 kg. It is essential to understand the rules for identifying significant figures to ensure accurate representation and communication of measurements in scientific and engineering contexts.