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Chapter 1: Problem 18

Round each number to the given place value. \(9817 ;\) hundreds

Short Answer

Expert verified
9800

Step by step solution

01

Identify the digit to round

Look at the number 9817. The digit in the hundreds place is 8.
02

Locate the digit to the right

Find the digit immediately to the right of the hundreds place. In this case, it is 1 in the tens place.
03

Determine whether to round up or down

Since the digit to the right (1) is less than 5, we do not round up. We keep the hundreds digit the same and change all digits to the right of it to zero.
04

Write the rounded number

The number 9817 rounded to the nearest hundred is 9800.

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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, helping us understand the value of each digit in a number based on its position. In the decimal system, each place represents a power of ten.
The rightmost digit is in the 'ones' place.
Moving left, we have the 'tens', 'hundreds', 'thousands', and so on.
For example, in the number 9817:
  • 7 is in the ones place.
  • 1 is in the tens place.
  • 8 is in the hundreds place.
  • 9 is in the thousands place.
Understanding place value helps in rounding numbers efficiently, by pinpointing which digit influences the rounding according to its position and the adjacent digits.
rounding rules
Rounding numbers simplifies them, making them easier to work with, especially during estimation.
Here are the essential rounding rules to follow:
  • Identify the place value to round to. This will be your focus digit.
  • Look at the digit immediately to the right of your focus digit (this is the deciding digit).
  • If the deciding digit is 5 or greater, round the focus digit up by one.
  • If the deciding digit is less than 5, keep the focus digit the same.
  • Change all digits to the right of the focus digit to zero.
Applying these rules ensures consistency and accuracy in rounding numbers.
hundreds place
When rounding to the hundreds place, our goal is to find the closest multiple of 100 to the given number.
In the number 9817, the hundreds place digit is 8.

Follow these steps:
  • Identify the hundreds place digit (8).
  • Look at the digit immediately to the right (1 in the tens place).
  • Because the deciding digit (1) is less than 5, keep the hundreds place digit the same (8).
  • Change all digits to the right of the hundreds place to zero.

Hence, 9817 rounded to the nearest hundred is 9800.

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