Obtain an estimate for the computation shown below by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in your head. Then use a calculator to perform the computation. How reasonable is the estimate when compared to the actual​ answer?

0.770.77times×306306

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Part 1

The estimate using rounded numbers is

enter your response here.

To estimate the product of \( 0.77 \times 306 \), we can round the numbers to values that are easier to multiply mentally:

1. Round \( 0.77 \) to \( 0.8 \).
2. Keep \( 306 \) as \( 300 \) for simplicity.

Now multiply:

\[
0.8 \times 300 = 240
\]

So, the estimate is \( 240 \).

### Now, let's compute the exact value using a calculator:

\[
0.77 \times 306 = 235.62
\]

### How reasonable is the estimate?

The estimate of \( 240 \) is quite close to the actual answer of \( 235.62 \). The rounding method provided a reasonable estimate that is within 2% of the exact value.

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Would you like more details or have any further questions?

Here are 5 related questions:
1. How does rounding affect the accuracy of an estimate?
2. When should you use rounding for mental calculations?
3. How can you choose the best rounding method for a given situation?
4. What is the significance of rounding in practical applications?
5. How do different rounding rules (e.g., rounding up or down) affect the outcome?

**Tip:** When estimating, try to round one number up and the other down to balance any potential overestimation or underestimation!

Obtain an estimate for the computation shown below by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in your head. Then use a calculator to perform the computation. How reasonable is the estimate when compared to the actual answer? 0.77 times 306

Learn how to estimate the product of 0.77 × 306 by rounding the numbers for easier mental arithmetic. Understand how close the estimate of 240 is compared to the exact value of 235.62, making this a practical problem for grades 5-7.

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