Addition and subtraction with significant figures | Decimals | Pre-Algebra | Khan Academy

Summary

The video script explains the concept of significant figures in mathematical operations. It clarifies that during multiplication and division, the result's precision is determined by the number with the least significant digits. For addition and subtraction, the precision depends on the least precise measurement involved. Examples illustrate how to round results to match the least precise value, emphasizing the importance of accuracy in representing measurements, including the use of scientific notation to denote significant figures.

Takeaways

• 📚 When multiplying or dividing, the result's number of significant digits is limited by the number with the fewest significant digits involved in the operation.
• 🔢 For example, multiplying 2.00 by 3.5 results in 7.00, which is rounded to 7.0 to maintain only 2 significant digits as per the smallest set in the multiplication.
• ➕➖ In addition and subtraction, the precision of the result is determined by the least precise measurement involved, not the number of significant digits.
• 📏 When adding measurements, if the least precise measurement is to the nearest tenth, the result should be rounded to the nearest tenth, regardless of the number of significant digits in the addends.
• 🧩 Real-world examples, such as carpet laying, may require rounding up due to practical considerations, but this is specific to certain contexts and not a general rule for significant figures.
• 📐 In measuring, if one measurement is more precise than the other, the combined measurement should reflect the precision of the least precise measurement to avoid misrepresentation.
• 📈 The concept of significant figures is not just about decimals; it applies to whole numbers as well, where precision is indicated by the place value measured to.
• 🔑 Scientific notation can be used to clearly indicate the precision of a measurement by showing the number of significant figures and the scale of the measurement.
• 📊 When combining measurements, it's crucial to round the result to the precision level of the least precise measurement to accurately represent the combined value.
• 📉 Rounding up or down is necessary when combining measurements to ensure the final result does not falsely imply a higher level of precision than was actually measured.
• 📝 Notation such as underlining the last significant digit or using scientific notation helps to clarify the precision of a measurement and the number of significant figures.

Q & A

What is the rule for determining significant figures when multiplying or dividing measurements?

The result of multiplication or division can only have as many significant figures as the measurement with the smallest number of significant figures involved in the operation.

Why is the significant figure rule different for addition and subtraction compared to multiplication and division?

For addition and subtraction, the precision of the result is determined by the least precise value in the operation, rather than the number of significant figures.

What is an example of how significant figures affect the result of a multiplication?

If you multiply 2.00 (2 significant figures) by 3.5 (3 significant figures), the result can only have 2 significant figures, which would be 7.0 when rounded to one decimal place.

How does the precision of measurements affect the result of an addition?

The result of an addition should be rounded to the same decimal place or counting unit as the least precise measurement in the operation.

What is the correct way to add 1.26 and 2.3, considering the precision of the measurements?

You add 1.26 and 2.3 to get 3.56, but since the least precise measurement is to the nearest tenth, you round the result to 3.6.

Why is it incorrect to add 1.901 meters and 2.09 meters to get 3.991 meters?

This is incorrect because it implies a precision to the nearest millimeter, whereas the second measurement was only precise to the nearest centimeter.

How should the height of two stacked blocks be calculated if one is measured to the nearest centimeter and the other to the nearest millimeter?

The total height should be calculated as 3.99 meters, rounded to the nearest hundredth, reflecting the precision of the least precise measurement.

What is the purpose of using scientific notation when expressing measurements with a specific level of precision?

Scientific notation clearly indicates the number of significant figures and the level of precision of the measurement by showing the decimal place relative to a power of ten.

How can you represent a measurement that is known to be precise to the nearest 10 feet?

You can represent it as 3.5 x 10^2 feet, indicating that there are two significant figures and the precision is to the nearest 10 feet.

What is the correct way to add the heights of a building measured to the nearest 10 feet and a tower measured to the nearest foot?

You would add 350 feet and 8 feet to get 358 feet, but then round to the nearest 10 feet to represent the least precise measurement, resulting in 360 feet.

Why is it important to consider the precision of measurements when performing arithmetic operations?

It is important to ensure that the result accurately reflects the level of precision of the original measurements and does not falsely imply a higher level of accuracy.