Benchmark Brilliance: How to Estimate Decimal Sums and Differences with Ease
Benchmarks are reference points that help us make quick estimates. Common benchmarks for decimals include \(0\), \(0.5\), and \(1\). By rounding decimals to these benchmarks, we can swiftly estimate their sums and differences. Let's delve into how to use benchmarks for estimating decimal operations.
Estimating Sums and Differences of Decimals Using Benchmarks
Example 1:
Estimate the sum of \(0.47\) and \(0.68\).
Estimation Process Using Benchmarks:
1. Round \(0.47\) to \(0.5\).
2. Round \(0.68\) to \(0.5\).
3. Estimate the sum: \(0.5 + 0.5 = 1\).
Answer:
The estimated sum is \(1\).
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Example 2:
Estimate the difference between \(0.72\) and \(0.29\).
Estimation Process Using Benchmarks:
1. Round \(0.72\) to \(0.5\).
2. Round \(0.29\) to \(0.5\).
3. Estimate the difference: \(0.5 – 0.5 = 0\).
Answer:
The estimated difference is \(0\).
Using benchmarks to estimate sums and differences of decimals provides a quick and intuitive approach to understanding the approximate outcome of operations. This method is especially useful when you need a general idea rather than precise calculations. By rounding to the nearest benchmark and then performing the operation, you can get a ballpark figure swiftly. Practice regularly to master this invaluable skill.
Practice Questions:
1. Estimate the sum of \(0.56\) and \(0.44\) using benchmarks.
2. What is the estimated difference between \(0.87\) and \(0.34\) using benchmarks?
3. Using benchmarks, estimate the sum of \(0.23\) and \(0.79\).
4. Estimate the difference between \(0.91\) and \(0.46\) using benchmarks.
5. Using benchmarks, what is the estimated sum of \(0.66\) and \(0.31\)?
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Answers:
1. \(1\)
2. \(0.5\)
3. \(1\)
4. \(0.5\)
5. \(1\)
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