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Chapter 4: Problem 72

Round each number to the given place value. 576 to the nearest hundred

Short Answer

Expert verified
576 rounded to the nearest hundred is 600.

Step by step solution

01

Identify the Hundreds and Tens Places

First, identify the hundreds and tens place in the number 576. The hundreds place is occupied by the digit 5, and the tens place is occupied by the digit 7.
02

Determine the Rounding Rule

According to the rounding rules, if the digit in the tens place is 5 or more, we round up. Since the tens digit is 7, which is more than 5, we will round up the hundreds digit.
03

Round the Hundreds Place

Since we round up, we increase the hundreds digit by 1. So, the digit in the hundreds place increases from 5 to 6.
04

Replace Tens and Units Places with Zeros

After rounding up the hundreds digit to 6, replace the digits in the tens and units position with zeros, resulting in the rounded number 600.

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Key Concepts

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

Nearest Hundred
Rounding to the nearest hundred means adjusting a number so that it is closest to a multiple of 100. For example, when rounding the number 576 to the nearest hundred, we check which multiple of 100 it is closest to. Consider the following steps:
  • First, look at the hundreds place of the number. In 576, this digit is 5.
  • Next, analyze the next immediate digit, which is in the tens place, to decide whether to round up or down.
This approach ensures the number becomes easier to work with, often simplifying math problems and estimates. Rounding to the nearest hundred is commonly used for estimating larger sums or simplifying complex calculations where exact precision isn't required.
Place Value
Understanding place value is crucial when rounding numbers. Place value determines the value of a digit in a number based on its position.
  • In the number 576, the digit 5 is in the hundreds place, indicating a value of 500.
  • The digit 7 is in the tens place, contributing a value of 70.
  • Finally, the digit 6 is in the units place, adding a value of 6.
To effectively round numbers, one must comprehend the contribution of each place and how changing a digit's position alters the number that it represents. This knowledge is essential in rounding exercises, as it enables the understanding of which digits to adjust or keep intact.
Rounding Rules
To ensure accuracy and consistency when rounding numbers, we follow specific rounding rules. Understanding these rules makes the rounding process clearer and helps avoid mistakes.
  • If the digit in the place immediately after the target rounding place (the deciding digit) is 5 or greater, we increase the target digit by 1.
  • If the deciding digit is less than 5, we keep the target digit the same.
In the example of rounding 576, the tens digit is 7. Since 7 is greater than 5, we round up the hundreds digit from 5 to 6. To complete the rounding, we replace all digits to the right of the hundreds place with zeros, resulting in 600. These rounding rules help ensure numbers are rounded consistently.

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Most popular questions from this chapter

$$\text { Evaluate each expression if } x=\frac{3}{4} \text { and } y=-\frac{4}{7}$$ $$x^{2}+7 y$$

Write each improper fraction as a mixed number or a whole number. See Example 21. $$\frac{225}{15}$$

Each expression contains one addition, one subtraction, one multiplication, and one division. Write the operations in the order that they should be performed. Do not actually simplify. $$\left(\frac{5}{6}-\frac{1}{3}\right) \cdot \frac{1}{3}+\frac{1}{2} \div \frac{9}{8}$$

Perform the indicated operations. $$ -5 \frac{1}{8}-19 \frac{3}{4} $$

In your own words, explain why \(\frac{0}{10}=0\) and \(\frac{10}{0}\) is undefined.
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