Question

The number of significant figures in \(0.0500\) is (1) one (2) three (3) two (4) four

Short answer

Three significant figures.

Step-by-step solution

Understand Significant Figures

Significant figures are the digits in a number that are known with certainty plus one estimated digit. This includes all non-zero digits, zeroes between significant figures, and trailing zeros in decimal numbers.

Analyze the Given Number

Look at the given number, 0.0500, and determine which digits are significant.

Identify the Non-Zero Digits

In 0.0500, the digits 5 and the trailing zeros after the decimal point are significant. The leading zeros are not significant as they only serve as placeholders.

Count the Significant Figures

Count 5 as one significant figure, and the trailing two zeros increase the count to three significant figures.

Key concepts

certainty in measurement

In any kind of measurement, there is always a degree of certainty and uncertainty. The digits that we are certain about in our measurements, plus one estimated digit, make up what are called significant figures. Knowing how to handle and identify significant figures helps ensure that our scientific and mathematical calculations maintain accuracy.

If, for instance, you measure something as 12.45 cm, here you are certain about 1, 2, and 4, and you estimate the digit 5. This means all these digits—1, 2, 4, and 5—are significant figures for this measurement. Recognizing which digits are certain and which are estimates is crucial in understanding and applying significant figures correctly.

non-zero digits

Non-zero digits are always significant because they are considered precise and provide meaningful information about the measured value. For example, in the number 123.45, each number (1, 2, 3, 4, and 5) contributes to the measurement's accuracy.

This means that if you see any number composed only of non-zero digits, you count them all as significant. Even when zeroes are placed between significant digits, such as in 102.304, those zeroes in between are significant as well. Therefore, the number 102.304 has six significant figures. Being able to recognize non-zero digits and their significance helps keep measurements precise and understood correctly.

trailing zeros

Trailing zeros refer to zeros that come after non-zero digits in a decimal number. These zeros are significant because they indicate a level of precision in the measurement. For example, the number 0.0500 has three significant figures—the digit 5 and the two trailing zeros.

Trailing zeros can only be significant if they come after a decimal point. This means that in a number like 4500, if written without a decimal, only the non-zero digits are automatically significant. However, if written as 4500., then all digits would be counted as significant, making it four significant figures.

It's also essential to distinguish between leading zeros and trailing zeros. Leading zeros are not significant—they merely act as placeholders. Understanding the significance of trailing zeros provides clarity for the level of accuracy in your measurements.