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Chapter 1: Problem 24

Round each of the numbers to the nearest hundred. $$6,778$$

Short Answer

Expert verified
6,778 rounded to the nearest hundred is 6,800.

Step by step solution

01

Understanding the Place Value

To round to the nearest hundred, focus on the hundreds place and the digit immediately to its right. In the number 6,778, "7" is in the hundreds place, and "7" is in the tens place.
02

Applying Rounding Rules

Check the digit in the tens place since it's 7, which is 5 or greater. According to rounding rules, if this digit is 5 or higher, we round the hundreds digit up.
03

Adjusting the Number

Increase the hundreds digit by 1. Change the digit at the hundreds place from "7" to "8" and set all digits to the right to zero to finish the rounding process.
04

Final Number after Rounding

After rounding, 6,778 to the nearest hundred becomes 6,800.

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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 a fundamental concept in mathematics that helps us understand the value and position of each digit in a number. It essentially defines how much a digit is worth based on its position within the number. For instance, in the number 6,778:
  • The digit "6" is in the thousands place, representing 6,000.
  • The first "7" is in the hundreds place, representing 700.
  • The second "7" is in the tens place, representing 70.
  • The "8" is in the ones place, representing 8.
Understanding the place value is crucial when rounding numbers because it directs our attention to the digits that will influence the rounding process. In rounding to the nearest hundred, our primary focus is on the hundreds place and the digit immediately to its right.
Rounding Rules
Rounding rules are a set of guidelines used to simplify numbers, making them easier to work with. The basic rule is straightforward:
  • Look at the digit to the right of the place value you're rounding to.
  • If this digit is 5 or greater, round the chosen place value digit up by 1.
  • If this digit is less than 5, keep the chosen place value digit unchanged.
For the example of 6,778, when rounding to the nearest hundred, we focus on the tens place, which is "7". Since "7" is greater than or equal to 5, we increase the hundreds digit "7" to "8". This simple rule helps ensure consistency and accuracy in rounding practices, allowing you to easily compute and estimate numbers.
Nearest Hundred
Rounding to the nearest hundred means adjusting a number to the closest hundred. This approach is often used to make calculations simpler without significantly affecting accuracy. The steps are as follows:
  • Identify the hundreds place and the number to its right.
  • Based on the rounding rules, decide if the hundreds digit stays the same or is increased by one.
  • The deciding digit here is the "7" in the tens position of 6,778, which results in rounding the hundreds digit "7" up to "8".
  • Finally, change all digits to the right of the hundreds place to zero.
Therefore, when rounding 6,778, we get 6,800 as the nearest hundred. This process simplifies the number significantly, making it more manageable for estimations and less detailed computations.

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