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Chapter 1: Problem 6

Round each whole number to the given place value. 8494 to the nearest hundred

Short Answer

Expert verified
8494 rounded to the nearest hundred is 8500.

Step by step solution

01

Understanding the Place Value

To begin, identify the digit in the hundreds place of the number 8494. When reading from left to right, the digits in 8494 are 8 (thousands), 4 (hundreds), 9 (tens), and 4 (ones). Therefore, the hundreds place is occupied by the digit 4.
02

Identify the Rounding Digit

Next, identify the digit to the immediate right of the hundreds place, which will determine whether we round up or stay the same. In 8494, the tens digit is 9.
03

Applying the Rounding Rule

According to rounding rules, if the digit to the right of the needed place value (in this case, the digit in the tens place) is 5 or more, you round up. Since 9 is greater than 5, we will round up the hundreds place digit.
04

Performing the Rounding

Increase the hundreds place digit by one. The original hundreds digit is 4, so increasing it by one results in 5. Therefore, 8494 rounded to the nearest hundred becomes 8500.

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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 of each digit in a number. Every digit in a number has a different weight depending on its position. From right to left, these positions include ones, tens, hundreds, thousands, and so forth. For example, in the number 8494, each digit represents:
  • 8 in the thousands place
  • 4 in the hundreds place
  • 9 in the tens place
  • 4 in the ones place

This means that each '4' represents a different value based on where it stands in the number. Understanding place value is crucial for rounding since it determines which digit we change and which digits we adjust accordingly.
Rounding Rules
Rounding is a useful process when you need to simplify numbers, making them easier to work with. The rules of rounding help us decide whether to increase or decrease a number's value. Here's the general rule:
  • If the digit to the right of your target place is 5 or more, round the target digit up.
  • If it's less than 5, you leave the target digit unchanged and shift the digits to the right to zeroes.

In our example of rounding 8494 to the nearest hundred, the target digit is '4' in the hundreds place. The next digit, a '9' in the tens place, is greater than 5. Therefore, we follow the rule of rounding up.
Whole Numbers
Whole numbers are simple numbers without fractions or decimals. They include zero and positive integers like 1, 2, 3, onwards. These numbers are used in everyday counting and arithmetic. Rounding becomes particularly relevant with whole numbers when we need to simplify calculations or estimate results quickly.

For example, if rounding 8494, a whole number, to the nearest hundred, we look at the complete number without splitting parts into decimal or fractional forms. Rounding helps people plan budgets, measure distances, and even keep scores in sports. By structuring a number to the nearest whole form, it becomes more digestible and practical for everyday use.

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