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Chapter 1: Problem 50

Estimate the products by rounding each factor to the nearest hundred. $$ 982 \times 650 $$

Short Answer

Expert verified
700,000

Step by step solution

01

Round 982 to the nearest hundred

Look at the tens digit of 982, which is 8. Since it is 5 or more, round 982 up to 1000.
02

Round 650 to the nearest hundred

Look at the tens digit of 650, which is 5. Since it is 5 or more, round 650 up to 700.
03

Multiply the rounded numbers

Multiply the rounded numbers from the previous steps: \[1000 \times 700 = 700,000.\]
04

Express the estimate

The estimated product of 982 and 650 by rounding each factor to the nearest hundred is 700,000.

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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 an essential mathematical skill that simplifies complex calculations. It involves adjusting a number to the nearest designated place value, making it easier to work with. The most common place values are tens, hundreds, thousands, and so on.
For example:
  • If you have a number like 982, the tens digit is 8.
  • Numbers with tens digits of 5 or more are rounded up. So, 982 rounds up to 1000.
Rounding helps create estimates that are close to the actual results but are much simpler to compute for quick mental calculations or checking results.
Nearest Hundred
Finding the nearest hundred of a number means determining which hundred a number is closest to. This is done by examining the tens digit of the number.
For example:
  • Consider the number 650. The tens digit is 5.
  • A tens digit of 5 or greater means you round up.
  • So, 650 rounds up to 700.
This technique is useful whenever you need to simplify numbers, especially in contexts like estimation, budgeting, or when precision is not required.
Multiplication Estimation
Multiplication estimation is a technique that allows for quicker calculations by using rounded numbers. Once the numbers are rounded, they can be easily multiplied to get an estimated product.
Let's take an example:
  • Using 982, which is rounded to 1000, and 650, which rounds to 700.
  • Multiply the rounded numbers: \[ 1000 \times 700 = 700,000. \]
Such estimation is beneficial for mental math calculations, allowing us to grasp the magnitude of the product without extensive computation. It's perfect for quick decision-making or when a rough calculation suffices.

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Most popular questions from this chapter

Without computing it, tell whether the average of \(126,135,198,\) and 113 is \(86 .\) Explain why it is possible or why it is not.

Find and correct the error when evaluating each expression for \(x=3\) and \(y=5 .\) \(\begin{aligned} 7 x+y^{2} &=7(3)+5^{2} \\ &=21+10 \\ &=31 \end{aligned}\)

Write each phrase as a variable expression. Use \(x\) to represent "a number." A number times twenty

The following table shows a few of the airports in the United States with the largest volumes of passengers. Complete this table. The first line is completed for you. (Source: Airports Council International) $$ \begin{array}{|l|c|c|c|c|} \hline & \text { Total passengers in 2015 } & \text { Amount Written } & \text { Standard Form } & \text { Standard Form } \\ & \text { (in hundred-thousands } & \text { in Standard } & \text { Rounded to the } & \text { Rounded to the } \\ \text { City Location of Airport } & \text { of passengers) } & \text { Form } & \text { Nearest Million } & \text { Nearest Ten-Million } \\ \hline \text { Atlanta, GA } & 1015 & 101,500,000 & 102,000,000 & 100,000,000 \\\ \hline \text { Dallas/Fort Worth, TX } & 641 & & & \\ \hline \end{array} $$

Write each phrase as a variable expression. Use \(x\) to represent "a number." A number subtracted from 11
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