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Chapter 3: Problem 63

Round to the nearest hundred: \(45,765 .\) [1.6a]

Short Answer

Expert verified
45,800

Step by step solution

01

Identify the Hundreds Place

Locate the digit in the hundreds place. In the number 45,765, the hundreds place is occupied by the digit 7.
02

Look at the Next Digit

Identify the digit immediately to the right of the hundreds place. In this case, the digit is 6.
03

Determine Rounding Rule

If the digit to the right of the hundreds place is 5 or greater, round up. If it is less than 5, round down. Since 6 is greater than 5, round up.
04

Round the Number

Change the hundreds place digit to the next higher digit and set all digits to its right to zero. Therefore, rounding 45,765 to the nearest hundred results in 45,800.

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Key Concepts

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

place value
Place value is essential in understanding how to round numbers. Every digit in a number has a specific place value. The place value tells you the value of the digit based on its position in the number.
If you look at the number 45,765:
  • The digit 5 is in the thousands place, so its value is 5,000.
  • The digit 7 is in the hundreds place, so its value is 700.
  • ... and so on.
Knowing place value helps you to identify which digit you will round and how it will impact the rest of the number.
rounding rules
Rounding rules are simple but important. They tell you when to round a number up and when to round it down. Here are the two main rules:
  • If the digit to the right of the rounding digit is 5 or greater, you round up.
  • If the digit is less than 5, you round down.
In our example, 45,765 is rounded to the nearest hundred. The digit in the hundreds place is 7, and the next digit to the right is 6. Since 6 is greater than 5, we follow the rule to round up. Therefore, 45,765 becomes 45,800.
basic mathematics
Basic mathematics is the foundation for many math skills, including rounding. Understanding addition, subtraction, multiplication, and division is crucial. Rounding is often used to make these calculations simpler and quicker.
In practical terms, rounding helps you estimate values to make mental math easier. For instance, instead of adding exact numbers like 1,489 and 2,312, you can round them to 1,500 and 2,300 for quicker estimation.
To summarize:
  • Knowing place value helps identify the rounding digit.
  • Following rounding rules tells you whether to round up or down.
  • Basic math skills help you understand and apply rounding in real-life situations.

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