The number 1.00310 has five significant figures. But which of the following numbers has the same number of significant figures? Let’s find out!

Answer: 1.00320

The number 1.00320 also has five significant figures. The zero at the end of the number is significant because it falls between two non-zero digits. When determining the number of significant figures in a measurement, it is important to consider all non-zero digits as well as any zeros between them.

Now, let’s take a closer look at why the number 1.00320 has the same number of significant figures as 1.00310 and also explore the concept of significant figures in more detail.

**What are significant figures?**

Significant figures, also known as significant digits, are the digits in a number that carry meaningful information. They are used to represent the precision or the accuracy of a measurement.

In simple terms, significant figures tell us how many digits in a number are known with certainty or are reliable. They provide a way to communicate the precision of a measurement and indicate the level of uncertainty associated with it.

**Rules for determining significant figures**

To determine the number of significant figures in a number, the following rules are generally followed:

1. Non-zero digits are always significant. For example, the number 345 has three significant figures.

2. Zeros between non-zero digits are always significant. For example, the number 102 has three significant figures.

3. Leading zeros (zeros to the left of the first non-zero digit) are not significant. For example, the number 0.008 has one significant figure.

4. Trailing zeros (zeros to the right of the non-zero digits) are significant if they are after a decimal point. For example, the number 10.00 has four significant figures.

5. Trailing zeros that are not after a decimal point may or may not be significant, depending on the context. It is best to clarify their significance if there is any ambiguity.

**Analyzing the number 1.00310**

Now, let’s break down why the number 1.00310 has five significant figures:

1. The digit 1 is a non-zero digit and is significant.

2. The digit 0 is a trailing zero, and it falls after the decimal point. Therefore, it is significant.

3. The digit 0 is a trailing zero, but it is not after the decimal point. In this case, its significance may be ambiguous. However, since there is a non-zero digit (3) after it, we consider it significant.

4. The digit 3 is a non-zero digit and is significant.

5. The digit 1 is a non-zero digit and is significant.

Therefore, the number 1.00310 has five significant figures.

**Exploring other numbers with the same significant figures**

To determine which numbers have the same number of significant figures as 1.00310, we need to consider the rules mentioned earlier.

Let’s analyze the options:

1. 100.310: This number has six significant figures. The leading zeros are not significant, but the non-zero digits (1, 0, 3, 1, and 0) are significant.

2. 0.0010031: This number has five significant figures. The leading zeros are not significant, and the non-zero digits (1, 0, 0, 3, and 1) are significant.

3. 10.0310: This number has six significant figures. The leading zero is not significant, and the non-zero digits (1, 0, 3, 1, and 0) are significant.

4. 1.00320: This number has five significant figures. The non-zero digits (1, 0, 0, 3, and 2) are significant.

As we analyzed earlier, the number 1.00320 has the same number of significant figures (five) as the number 1.00310.

**Frequently Asked Questions**

**Q: Why are significant figures important?**

A: Significant figures are important because they convey the precision and accuracy of a measurement. They indicate the number of digits known with certainty and help avoid overrepresentation of measurement precision.

**Q: How do significant figures affect calculations?**

A: When performing calculations, it is necessary to consider the significant figures of the numbers involved. The result of a calculation should be expressed with the same number of significant figures as the least precise measurement used in the calculation.

**Q: Are there any exceptions to the rules for significant figures?**

A: Yes, in certain cases, scientific notation is used to express numbers with a specific number of significant figures. In scientific notation, the number is written as a coefficient multiplied by a power of ten, allowing for clear representation of significant figures.

**Final Thoughts**

Understanding significant figures is crucial for anyone involved in scientific or mathematical work. These concepts help ensure the accuracy and precision of measurements and calculations while effectively communicating the level of uncertainty associated with the data.

By adhering to the rules for determining significant figures, one can ensure that the right level of precision is maintained throughout scientific experiments, calculations, and data reporting. So, the next time you encounter a number with a specific number of significant figures, remember the rules and how they define the reliability and precision of the measurement.