Which of the following numbers has three significant figures? This is a common question that arises in scientific calculations and everyday life. Significant figures are crucial in determining the precision and accuracy of measurements, and understanding how to identify them is essential for anyone working with numbers.
In this article, we will explore the concept of significant figures, their importance, and how to determine which of the given numbers has three significant figures. We will also discuss the rules for counting significant figures and provide examples to illustrate these rules.
Significant figures are digits in a number that carry meaning in terms of precision. They are used to indicate the level of accuracy of a measurement. For instance, the number 123.45 has five significant figures, while the number 123 has three significant figures. The distinction between these two numbers is crucial when performing calculations and reporting results.
To determine the number of significant figures in a given number, we must follow a set of rules:
1. All non-zero digits are significant. For example, 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 before the first non-zero digit) are not significant. For example, in the number 0.0045, the first two zeros are not significant, but the last two digits (4 and 5) are significant.
4. Trailing zeros (zeros after the last non-zero digit) are significant if they are to the right of the decimal point. For example, in the number 0.000045, all five digits are significant. However, if the number is 4500, the trailing zeros are not significant.
5. In scientific notation, all digits are significant. For example, in the number 2.5 x 10^3, both 2 and 5 are significant.
Now, let’s apply these rules to the question at hand: which of the following numbers has three significant figures?
1. 123.45 – This number has five significant figures.
2. 0.0045 – This number has two significant figures.
3. 1001 – This number has four significant figures.
4. 4500 – This number has one significant figure.
5. 2.5 x 10^3 – This number has two significant figures.
Based on the rules for counting significant figures, the number 4500 does not have three significant figures. Therefore, none of the given numbers have three significant figures. It is essential to understand the rules for identifying significant figures to ensure accurate calculations and data reporting in various fields.
