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Chapter 0: Problem 31

$$ \text { Round } 65,432 \text { to the nearest thousand. } $$

Short Answer

Expert verified
65,000

Step by step solution

01

Identify the thousands place

Look at the digit in the thousands place. In the number 65,432, the thousands place is occupied by the digit 5.
02

Look at the digit to the right

Examine the digit immediately to the right of the thousands place digit. This digit is called the hundreds place. In this case, it is the digit 4.
03

Apply rounding rules

Use the rounding rule: if the hundreds place digit is 5 or greater, round up the thousands place digit. If it is less than 5, keep the thousands place digit the same. Since the digit is 4, which is less than 5, keep the thousands place digit as it is.
04

Set the remaining digits to zero

Change all digits to the right of the thousands place to zero. Therefore, 65,432 becomes 65,000.

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Key Concepts

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

rounding rules
Rounding is a mathematical technique used to simplify numbers. This makes them easier to work with. The key to rounding lies in understanding and applying rounding rules.

When rounding a number, you need to look at the digit to the right of the place you are rounding to. Here are the basic rules:

  • If the digit is 5 or greater, round the number up.
  • If the digit is less than 5, round the number down (or keep it the same).

For example, when rounding 65,432 to the nearest thousand, the digit to the right of the thousands place (5) is 4. Since 4 is less than 5, we keep the thousands place digit (5) as it is, resulting in 65,000.
place value
Understanding place value is essential when rounding numbers or performing any numerical operation. Each digit in a number has a specific place value based on its position.

Let's break down the number 65,432:
  • '6' is in the ten-thousands place.
  • '5' is in the thousands place.
  • '4' is in the hundreds place.
  • '3' is in the tens place.
  • '2' is in the ones place.

When we say 'round to the nearest thousand,' we focus on the thousands place. In our example, we look at the digit 5. To determine whether to round up or down, we look at the digit in the hundreds place, which is 4.
nearest thousand
Rounding to the nearest thousand means adjusting a number so that it is closer to the nearest thousand. This is particularly useful for estimation or simplifying large numbers.

To round 65,432 to the nearest thousand, follow these steps:
  • Identify the digit in the thousands place (the 5 in 65,432).
  • Look at the digit to the right of it (the 4 in the hundreds place).
  • Apply the rounding rules:
    • If the hundreds digit is 5 or more, increase the thousands place digit by 1.
    • If the hundreds digit is less than 5, leave the thousands place digit as is.
  • Replace the digits to the right of the thousands place with zeroes.

Therefore, since 4 is less than 5, 65,432 rounded to the nearest thousand becomes 65,000.

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Most popular questions from this chapter

For exercises 1-80, evaluate. $$ (18-12) \div 2+1 $$

For exercises \(13-24\), rewrite the fraction as a decimal number. $$ \frac{8}{5} $$

For exercises \(47-58\), rewrite the percent as a decimal number. $$ 8.4 \% $$

$$ \text { Round } 0.2394 \text { to the nearest hundredth. } $$

For exercises 101-104, evaluate. Use a scientific or a graphing calculator. $$ -80 \div(-2)+4(-6)^{2} $$
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