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Chapter 5: Problem 66

Round each decimal to the given place value. \(68,934.543,\) nearest ten

Short Answer

Expert verified
The number rounded to the nearest ten is 68,930.

Step by step solution

01

Identify the Digit in the 'Tens' Place

First, look at the number 68,934.543 and identify the digit in the 'tens' place. In the number 68,934.543, the 'tens' digit is 3 since we are rounding to the nearest ten.
02

Look at the Next Smallest Place Value

Examine the digit to the right of the 'tens' place, which is the 'ones' place. In 68,934.543, the 'ones' digit is 4.
03

Apply Rounding Rule

Apply the rounding rule: If the 'ones' digit is 5 or greater, increase the 'tens' digit by 1. If it is less than 5, keep the 'tens' digit the same. Here, since 4 is less than 5, the 'tens' digit remains 3.
04

Replace Remaining Digits with Zeros

Since we're rounding to the nearest ten, replace all digits to the right of the 'tens' place with zeros. This changes our number from 68,934.543 to 68,930.

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Key Concepts

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

Place Value
The place value of a digit in a number tells us how much that digit is worth. In the number 68,934.543, each digit has a specific place value:
  • 6 is in the 'ten thousands' place, valued at 60,000
  • 8 is in the 'thousands' place, valued at 8,000
  • 9 is in the 'hundreds' place, valued at 900
  • 3 is in the 'tens' place, valued at 30
  • 4 is in the 'ones' place, valued at 4
  • 5 is in the 'tenths' place after the decimal
  • 4 is in the 'hundredths' place
  • 3 is in the 'thousandths' place
Understanding the place value is crucial when rounding numbers, as it helps us to determine which digit to focus on and how to adjust the number.
Decimal Rounding
Decimal rounding simplifies numbers by reducing the number of digits. The goal is to keep the number's value approximately the same but easier to use. In our exercise, we rounded the number 68,934.543 to the nearest ten, simplifying calculations. Here's a quick look at the rounding process:
  • Identify the digit at the specified place value (e.g., 'tens' place)
  • Look at the digit immediately to the right
  • Decide whether to round up or stay the same
When rounding decimals, understanding which place value you are rounding to dictates the accuracy level you wish to maintain.
Rounding Rules
Rounding rules help decide whether you increase the rounding digit or leave it the same. When considering the rules:
  • Look at the next smallest place value digit
  • If this digit is 5 or greater, increase the rounding digit by one
  • If it is less than 5, leave the rounding digit unchanged
In our case with 68,934.543, the 'tens' digit (3) is determined by looking at the 'ones' digit (4). Since 4 is less than 5, the 'tens' digit stays at 3, and any subsequent digits are replaced by zeros. Mastering these rules enables precise control over rounding decisions in various calculations.

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