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Chapter 1: Problem 10

Round each whole number to the given place value. 82,198 to the nearest thousand

Short Answer

Expert verified
82,198 rounded to the nearest thousand is 82,000.

Step by step solution

01

Identify the place value

To round 82,198 to the nearest thousand, first identify the digits that make up the 'thousands' place. In the number 82,198, the digit in the thousands place is '2', found in the position four digits from the right.
02

Look at the next smallest place value

After identifying the 'thousands' place, look at the digit to the immediate right, which is the 'hundreds' place. In 82,198, the 'hundreds' digit is '1'.
03

Determine whether to round up or down

If the digit in the hundreds place is 5 or higher, increase the thousands place digit by one. If it is lower than 5, keep the thousands place the same. Here, since the hundreds digit is '1', which is less than 5, round down.
04

Replace the following digits with zeros

To complete the rounding, replace all digits to the right of the 'thousands' digit with zeros. Therefore, 82,198 rounded to the nearest thousand is '82,000'.

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Key Concepts

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

Place Value
Understanding place value is essential when working with numbers, particularly in rounding. Place value refers to the position of a digit in a number, determining its value. For example, in the number 82,198:
  • The digit '8' is in the ten thousands place.
  • '2' is in the thousands place.
  • '1' is in the hundreds place.
  • '9' is in the tens place.
  • '8' is in the units place.
These positions tell us how much each digit contributes to the overall number. In our case, the place value of 2 is crucial since it represents two thousand. Knowing place values helps identify which digit to focus on when rounding a number.
Whole Numbers
Whole numbers are numbers without fractions or decimals. They are the basic building blocks of mathematics. Examples include numbers like 0, 1, 2, 3, and so on. When rounding whole numbers, we aim to approximate them to a desired place value, creating a simpler, yet similarly valued number.
Whole numbers can be easily rounded because they don鈥檛 contain fractional parts. In our example, 82,198 is a whole number. Understanding that it's made purely of integers, we can apply rounding rules without worrying about additional decimal places.
All discussions about place value and rounding rules are usually applied to whole numbers in basic calculations and everyday problem-solving.
Thousands Rounding
Thousands rounding involves adjusting a number to the closest multiple of one thousand. It's a common practice in estimation to make numbers easier to handle or understand. To round to the nearest thousand, focus on the thousands digit, then look at the digit directly to its right (the hundreds place).
The steps include:
  • Identify the thousands place. In 82,198, it's the second digit from the left: '2'.
  • Examine the hundreds place, which is '1'.
  • If the hundreds digit is 5 or more, round the thousands place digit up by one. If less, keep it unchanged. Since '1' is less than 5, '2' remains the same.
  • Replace any digits after the thousands digit with zeros. So, 82,198 becomes 82,000.
This approach helps us present an approximate value that is easy to comprehend, best for quick considerations and estimates.

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Most popular questions from this chapter

Match each word phrase to the correct translation. a. \(20 \div 200\) b. \(200 \div 20\) c. \(40 \div 8\) d. \(8 \div 40\) The quotient of 40 and 8.

The following table shows the top five automakers and the amount of money they spent on U.S. television advertising during a recent year. Use this table to answer Exercises 111 and 112. (Source: Automotive News) $$\begin{array}{|l|c|}\hline & \begin{array}{c}\text { Amount Spent on Television } \\\\\text { Advertising During a Recent Year }\end{array} \\\\\hline \text { General Motors } & \$ 3,500,000,000 \\\\\hline \text { Ford } & \$ 2,680,000,000 \\\\\hline \text { Fiat Chrysler Automobiles } & \$ 2,250,000,000 \\\\\hline \text { Toyota } & \$ 1,800,000,000 \\\\\hline \text { Nissan } & \$ 1,140,000,000 \\\\\hline\end{array}$$ Find the average amount of money spent on television ads by the top four advertisers.

Check each addition below. If it is incorrect, find the correct answer. $$ \begin{array}{r} 773 \\ 659 \\ +481 \\ \hline 1913 \end{array} $$

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) $$ \begin{array}{|l|c|c|c|c|} \hline & \text { Total passengers in 2015 } & \text { Amount Written } & \text { Standard Form } & \text { Standard Form } \\ & \text { (in hundred-thousands } & \text { in Standard } & \text { Rounded to the } & \text { Rounded to the } \\ \text { City Location of Airport } & \text { of passengers) } & \text { Form } & \text { Nearest Million } & \text { Nearest Ten-Million } \\ \hline \text { Atlanta, GA } & 1015 & 101,500,000 & 102,000,000 & 100,000,000 \\\ \hline \text { Chicago, IL } & 769 & & & \\ \hline \end{array} $$

Perform each indicated operation. Watch the operation symbol. $$304 \div 31$$
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