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Understanding Significant Digits

Significant digits are the numbers in a measurement that are known to be reliable and certain. They are used to express the precision of a measurement. When measurements are added or subtracted, the number of significant digits in the answer is determined by the measurement with the fewest significant digits.

Rules for Significant Digits in Addition and Subtraction

  1. When adding or subtracting measurements, the answer should have the same number of decimal places as the measurement with the fewest decimal places.
  2. When adding or subtracting measurements, the answer should have the same number of significant digits as the measurement with the fewest significant digits.

Example 1: Adding Measurements

  • Measurement 1: 4.920 g
  • Measurement 2: 1.20 g

To add these measurements, we need to line up the decimal points and add the numbers.

4.920 g + 1.20 g = 6.120 g

Since Measurement 2 has only 2 significant digits, the answer should also have 2 significant digits.

6.120 g ≈ 6.1 g

Example 2: Subtracting Measurements

  • Measurement 1: 4.920 g
  • Measurement 2: 1.20 g

To subtract these measurements, we need to line up the decimal points and subtract the numbers.

4.920 g - 1.20 g = 3.720 g

Since Measurement 2 has only 2 significant digits, the answer should also have 2 significant digits.

3.720 g ≈ 3.7 g

Example 3: Adding Measurements with Different Numbers of Significant Digits

  • Measurement 1: 4.920 g (3 significant digits)
  • Measurement 2: 1.20 g (2 significant digits)

To add these measurements, we need to line up the decimal points and add the numbers.

4.920 g + 1.20 g = 6.120 g

Since Measurement 2 has only 2 significant digits, the answer should also have 2 significant digits.

6.120 g ≈ 6.1 g

Example 4: Subtracting Measurements with Different Numbers of Significant Digits

  • Measurement 1: 4.920 g (3 significant digits)
  • Measurement 2: 1.20 g (2 significant digits)

To subtract these measurements, we need to line up the decimal points and subtract the numbers.

4.920 g - 1.20 g = 3.720 g

Since Measurement 2 has only 2 significant digits, the answer should also have 2 significant digits.

3.720 g ≈ 3.7 g

Conclusion

When adding or subtracting measurements, the number of significant digits in the answer is determined by the measurement with the fewest significant digits. By following the rules for significant digits in addition and subtraction, we can ensure that our answers are accurate and reliable.

Key Takeaways

  • When adding or subtracting measurements, the answer should have the same number of decimal places as the measurement with the fewest decimal places.
  • When adding or subtracting measurements, the answer should have the same number of significant digits as the measurement with the fewest significant digits.
  • The number of significant digits in the answer is determined by the measurement with the fewest significant digits.

Practice Problems

  1. Add the following measurements: 2.456 g + 1.20 g
  2. Subtract the following measurements: 4.920 g - 1.20 g
  3. Add the following measurements: 3.456 g + 2.10 g
  4. Subtract the following measurements: 2.456 g - 1.20 g

Answer Key

  1. 3.656 g ≈ 3.7 g
  2. 3.720 g ≈ 3.7 g
  3. 5.556 g ≈ 5.6 g
  4. 1.256 g ≈ 1.3 g
    Counting Significant Digits When Measurements are Added or Subtracted: Q&A ====================================================================

Q: What are significant digits?

A: Significant digits are the numbers in a measurement that are known to be reliable and certain. They are used to express the precision of a measurement.

Q: Why are significant digits important?

A: Significant digits are important because they help us determine the accuracy of a measurement. By following the rules for significant digits in addition and subtraction, we can ensure that our answers are accurate and reliable.

Q: What are the rules for significant digits in addition and subtraction?

A: The rules for significant digits in addition and subtraction are:

  1. When adding or subtracting measurements, the answer should have the same number of decimal places as the measurement with the fewest decimal places.
  2. When adding or subtracting measurements, the answer should have the same number of significant digits as the measurement with the fewest significant digits.

Q: How do I determine the number of significant digits in an answer?

A: To determine the number of significant digits in an answer, you need to look at the measurement with the fewest significant digits. The answer should have the same number of significant digits as this measurement.

Q: What if I have measurements with different numbers of significant digits?

A: If you have measurements with different numbers of significant digits, you need to follow the rules for significant digits in addition and subtraction. The answer should have the same number of significant digits as the measurement with the fewest significant digits.

Q: Can I round my answer to the correct number of significant digits?

A: Yes, you can round your answer to the correct number of significant digits. However, you should only round to the correct number of significant digits if the answer is exact. If the answer is not exact, you should not round it.

Q: What if I have a measurement with a trailing zero?

A: If you have a measurement with a trailing zero, you need to consider whether the zero is significant or not. If the zero is not significant, you can ignore it. However, if the zero is significant, you need to include it in the measurement.

Q: Can I use significant digits in multiplication and division?

A: Yes, you can use significant digits in multiplication and division. However, the rules for significant digits in multiplication and division are different from the rules for addition and subtraction. In multiplication and division, the answer should have the same number of significant digits as the measurement with the fewest significant digits.

Q: What if I have a measurement with a decimal point?

A: If you have a measurement with a decimal point, you need to consider whether the decimal point is significant or not. If the decimal point is not significant, you can ignore it. However, if the decimal point is significant, you need to include it in the measurement.

Q: Can I use significant digits in scientific notation?

A: Yes, you can use significant digits in scientific notation. However, the rules for significant digits in scientific notation are different from the rules for addition and subtraction. In scientific notation, the answer should have the same number of significant digits as the measurement with the fewest significant digits.

Conclusion

Significant digits are an important concept in measurement and calculation. By following the rules for significant digits in addition and subtraction, we can ensure that our answers are accurate and reliable. Remember to always consider the number of significant digits in your measurements and to round your answers to the correct number of significant digits.

Key Takeaways

  • Significant digits are the numbers in a measurement that are known to be reliable and certain.
  • The rules for significant digits in addition and subtraction are:
    1. When adding or subtracting measurements, the answer should have the same number of decimal places as the measurement with the fewest decimal places.
    2. When adding or subtracting measurements, the answer should have the same number of significant digits as the measurement with the fewest significant digits.
  • The number of significant digits in an answer is determined by the measurement with the fewest significant digits.
  • You can round your answer to the correct number of significant digits if the answer is exact.
  • You can use significant digits in multiplication and division, but the rules are different from the rules for addition and subtraction.

Practice Problems

  1. Add the following measurements: 2.456 g + 1.20 g
  2. Subtract the following measurements: 4.920 g - 1.20 g
  3. Add the following measurements: 3.456 g + 2.10 g
  4. Subtract the following measurements: 2.456 g - 1.20 g

Answer Key

  1. 3.656 g ≈ 3.7 g
  2. 3.720 g ≈ 3.7 g
  3. 5.556 g ≈ 5.6 g
  4. 1.256 g ≈ 1.3 g