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Chapter 1: Problem 34

Round each of the numbers to the nearest thousand. $$567$$

Short Answer

Expert verified
567 rounded to the nearest thousand is 0.

Step by step solution

01

Identify the Thousands Place

Look at the number given, which is 567. Determine the thousands place, which for this number is nonexistent since it is a three-digit number.
02

Check If Rounding is Possible

Since 567 is less than 1000, we cannot round to the nearest thousand. Any attempt to do so will naturally lead to zero because it isn't large enough to reach 1000.

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Key Concepts

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

Understanding Place Value
Place value is a fundamental concept in mathematics that helps us understand the value of digits within a number. Each digit in a number has its own place value, depending on its position. For example, in the number 567:
  • The "7" is in the ones place and represents 7.
  • The "6" is in the tens place and represents 60.
  • The "5" is in the hundreds place and represents 500.
Notice that there is no digit in the thousands place. If a digit were there, it would represent thousands of units. Understanding place value allows us to read, write, and work with numbers more effectively. This is crucial for operations like rounding, where we decide the significance of keeping or altering certain digits based on their position.
Rounding Rules Simplified
Rounding numbers involves the process of approximating a number to make it simpler, yet still close to the original value. The rules for rounding numbers can vary, but a common method is to look at the digit to the right of the place value to which you're rounding. To round numbers correctly:
  • Find the targeted place value (e.g., thousands place).
  • Check the digit immediately to its right.
  • If that digit is 5 or greater, increase the targeted place value by one.
  • If it's less than 5, keep the targeted digit unchanged.
  • Change all digits to the right of the targeted place value to zero.
In the case of rounding a three-digit number like 567 to the nearest thousand, it's essential first to identify if rounding is possible. Since a three-digit number doesn't have a thousands place, rounding would result in zero because it's impossible for it to be close to 1000. Therefore, since the number 567 is closer to zero than to 1000, it rounds down to zero.
Building Number Sense Through Rounding
Number sense refers to one鈥檚 ability to understand and work with numbers. It involves recognizing numbers, their values, and the way they relate to each other. A strong sense of numbers aids in rounding, estimation, and mental calculations. When dealing with questions like rounding 567 to the nearest thousand, developing number sense can help recognize why it doesn't make sense to do so.
  • Recognize that 567 is much less than 1000, hence why it typically "rounds" to zero.
  • Understand the practical use of rounding in estimating and simplifying calculations when dealing with numbers in real-life scenarios.
Fostering a good number sense ensures a profound comprehension of mathematics beyond memorizing rules. It enhances one's ability to approach problems intuitively, allowing for smarter, faster calculations and better decision-making skills in everyday life.

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Most popular questions from this chapter

Add each of the following. (All problems involve carrying in at least one column. $$\begin{array}{l} 52,468 \\ 58,642 \\ \hline \end{array}$$

Add each of the following. (All problems involve carrying in at least one column. $$\begin{array}{r} 6,824 \\ 371 \\ 4,857 \\ \hline \end{array}$$

Write each of the following in symbols. a. The sum of 4 and 8 is 12 b. The sum of \(a\) and \(b\) is 6

Add each of the following. (There is no carrying involved in these problems. $$\begin{array}{r} 6,245 \\ 203 \\ 1,001 \\ \hline \end{array}$$

Write each of the following in symbols. a. The sum of 5 and 2 b. 3 added to 8
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