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When Reported to the Correct Number of Significant Digits, the Product of 0.01200 and 45.9 Is?

Significant digits play a crucial role in accurately reporting measurements and calculations. They help convey the precision and reliability of a value. When dealing with multiplication or division, it becomes essential to maintain the correct number of significant digits to ensure the accuracy of the final result. In this article, we will explore the significance of reporting the product of 0.01200 and 45.9 to the correct number of significant digits.

To understand the importance of significant digits, let’s first define what they are. Significant digits, also known as significant figures, are the digits in a number that carry meaning concerning its precision. They include all non-zero digits and any zeros between non-zero digits. However, leading zeros (zeros before the first non-zero digit) are not considered significant. In our case, the number 45.9 has three significant digits, while 0.01200 has five significant digits.

When multiplying two numbers, the general rule is to report the final result with the same number of significant digits as the least precise number involved in the calculation. In our case, 45.9 has three significant digits, making it the least precise number in the multiplication.

To find the product of 0.01200 and 45.9, we perform the multiplication as follows:

0.01200 x 45.9 = 0.5508

Now, we need to determine the correct number of significant digits in the product. Since 45.9 has three significant digits, the final result should also be reported with three significant digits. Therefore, the product of 0.01200 and 45.9, when reported to the correct number of significant digits, is 0.551.

FAQs:

Q: Why is it important to report the product to the correct number of significant digits?

A: Reporting the product to the correct number of significant digits ensures that the result is conveyed with the appropriate level of precision. It provides information about the reliability of the measurement or calculation.

Q: What happens if the product is reported with more significant digits than necessary?

A: Reporting with more significant digits than necessary can give the false impression of increased precision. It may imply a level of accuracy that is not actually present in the measurement or calculation.

Q: Can you round off the product to fewer significant digits than the least precise number involved in the calculation?

A: No, it is not advisable to round off the product to fewer significant digits than the least precise number. Doing so would result in a loss of essential information about the precision of the measurement or calculation.

Q: What if both numbers involved in the multiplication have the same number of significant digits?

A: In such cases, the product should be reported with the same number of significant digits as the original numbers. This maintains consistency and ensures that the precision of the final result is accurately conveyed.

Q: Are significant digits only important in multiplication and division?

A: No, significant digits are important in all mathematical operations, including addition and subtraction. They help maintain the appropriate level of precision throughout calculations.

In conclusion, when reporting the product of 0.01200 and 45.9 to the correct number of significant digits, it is crucial to consider the least precise number involved in the multiplication. In this case, 45.9 has three significant digits, indicating that the final result should also be reported with three significant digits. Paying attention to significant digits allows us to accurately convey the precision and reliability of measurements and calculations, ensuring the integrity of scientific data.

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