/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 52 Estimate each product. $$2 \cd... [FREE SOLUTION] | 91影视

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Chapter 11: Problem 52

Estimate each product. $$2 \cdot 1.7 \cdot 9$$

Short Answer

Expert verified
The estimated product is 36.

Step by step solution

01

Round the Numbers

Begin by rounding each number to a whole number to make estimation easier. \(2\) stays the same, \(1.7\) rounds to \(2\), and \(9\) stays the same.
02

Calculate the Product of Rounded Numbers

Multiply the rounded numbers: \(2 \cdot 2 \cdot 9 = 36\). This product is an estimate of the original multiplication problem.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Rounding Numbers
Rounding numbers is a technique used to simplify mathematical calculations by adjusting numbers to their nearest whole or significant values. This helps make arithmetic processes quicker and easier to handle, especially when estimating.

To round a number, you need to look at the digit just after the place you want to round to.
  • If this digit is 5 or higher, you increase the rounding digit by one.
  • If it's less than 5, you leave the rounding digit unchanged.
In our example, we rounded 1.7 to 2. This is because the digit after the whole number place is 7, which is greater than 5. Therefore, we increase the whole number part from 1 to 2. Rounding numbers is essential for estimating products as it simplifies numbers, making calculations more manageable and less prone to error.
Whole Numbers
Whole numbers are numbers without fractions or decimals. They start from zero and go upwards: 0, 1, 2, 3, and so on. In the context of multiplication estimation, whole numbers are helpful because they are simpler to work with than numbers with decimal parts.

When estimating, we often round numbers to the nearest whole number, as seen in our problem with rounding 1.7 to 2. By converting numbers into whole numbers, we can perform calculations in our head or on paper more quickly.

Whole numbers are fundamental in basic math calculations, and understanding them is critical to solving many math problems, especially those that involve estimation.
Multiplication Estimation
Multiplication estimation is a method used to quickly approximate the result of a multiplication problem without needing exact calculations. By using rounded numbers, we simplify the multiplication process.

For instance, the original problem involves multiplying three numbers: 2, 1.7, and 9. By rounding 1.7 to 2, we transform the multiplication into a more straightforward problem of multiplying three whole numbers: 2, 2, and 9.

The steps are simple:
  • Round each number to a whole number.
  • Multiply the rounded numbers together.
This leads to a result of 36, which is a quick estimate of the original product. This method is particularly useful in situations where an approximate answer is sufficient, and it saves time and effort in complex calculations.

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Most popular questions from this chapter

Determine whether each pair of solids is sometimes, always, or never similar. Explain. two cubes

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