Verified Answer :

  • Identify the tenths and hundredths digits for \(12.24\) and \(4.614\).
  • Round each number to the nearest tenth by applying the rule for rounding based on the hundredths digit.
  • Sum the rounded values \(12.2\) and \(4.6\).
  • The final estimated sum is \(\boxed{16.8}\).

Explanation

  1. Analyzing the Rounding Rules

To estimate the sum \(12.24 + 4.614\) by rounding each number to the nearest tenth, we first examine the digits of each number. Rounding to the nearest tenth involves looking at the digit in the hundredths place to decide whether to round the tenths digit up or leave it unchanged. If the digit in the hundredths place is less than 5, we round down, keeping the tenths digit as it is. If it is 5 or greater, we increment the tenths digit by 1.

  1. Rounding the Given Numbers

For the number \(12.24\), the digit in the tenths place is 2 and the digit in the hundredths place is 4. Since 4 is less than 5, we keep the tenths digit unchanged. Thus, \(12.24\) rounded to the nearest tenth is \(12.2\). For the number \(4.614\), the digit in the tenths place is 6 and the digit in the hundredths place is 1. Since 1 is less than 5, we keep the tenths digit unchanged. Thus, \(4.614\) rounded to the nearest tenth is \(4.6\).

  1. Calculating the Estimated Sum

Now that we have the rounded values, we calculate the estimated sum:
\[12.2 + 4.6 = 16.8\]
Therefore, the estimated sum of \(12.24 + 4.614\) rounded to the nearest tenth is \(\boxed{16.8}\).

Examples

Rounding is a common practice in everyday life, such as when estimating the total cost of groceries at a store. If an item costs \(\$12.24\) and another costs \(\$4.614\), you might round them to \(\$12.20\) and \(\$4.60\) to quickly estimate that the total is approximately \(\$16.80\). This helps in managing budgets and making quick mental calculations when exact precision is not immediately required.

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