Verified Answer :

  • Round \(13.87\) to the nearest tenth: \(13.9\).
  • Round \(6.541\) to the nearest tenth: \(6.5\).
  • Subtract the rounded values: \(13.9 - 6.5 = 7.4\).
  • The final estimate is \(\boxed{7.4}\).

Explanation

  1. Problem Analysis and Rounding Rules

To estimate the value of \(13.87 - 6.541\), we follow a two-step process. First, we round each number to the nearest tenth according to the standard rounding rule: if the digit in the hundredths place is 5 or greater, round the tenths digit up by 1; if it is less than 5, keep the tenths digit as it is. Then, we perform the subtraction with these rounded values.

  1. Rounding the Numbers

For the first number, \(13.87\), the tenths digit is 8 and the hundredths digit is 7. Since 7 is greater than or equal to 5, we round the tenths digit up from 8 to 9. Thus, \(13.87\) rounds to \(13.9\).

For the second number, \(6.541\), the tenths digit is 5 and the hundredths digit is 4. Since 4 is less than 5, we keep the tenths digit as 5. Thus, \(6.541\) rounds to \(6.5\).

  1. Final Calculation and Result

Now we subtract the rounded values:
\[13.9 - 6.5 = 7.4\]
The estimated value of the original expression is 7.4.

Examples

Rounding is a fundamental skill used in everyday life to quickly estimate quantities. For instance, when grocery shopping, if you have a budget of \(\$50\) and items cost \(\$13.87\) and \(\$6.54\), you can quickly estimate their difference or total cost by rounding to the nearest tenth or dollar to keep a running tally in your head without needing a calculator. This ensures you stay within your budget while shopping efficiently.

Related Questions