Verified Answer :

  • Round each term to one significant figure: \(4.3 \approx 4\), \(7.5 \approx 8\), and \(1.7 \approx 2\).
  • Substitute these into the expression: \(\frac{4 + 8}{2}\).
  • Add the numbers in the numerator: \(4 + 8 = 12\).
  • Divide by the denominator to find the final estimate: \(\frac{12}{2} = 6\).
  • The final estimated value is \(\boxed{6}\).

Explanation

  1. Rounding to One Significant Figure

To estimate the value of the expression \(\frac{4.3 + 7.5}{1.7}\) by rounding to one significant figure, we must first identify the first non-zero digit of each number and evaluate the following digit to decide whether to round down or round up.

  1. For 4.3, the first significant figure is 4. Since the next digit is 3 (which is less than 5), we keep the 4 as is. Thus, 4.3 rounds to 4.
  2. For 7.5, the first significant figure is 7. Since the next digit is 5 (which is 5 or greater), we round the 7 up to 8. Thus, 7.5 rounds to 8.
  3. For 1.7, the first significant figure is 1. Since the next digit is 7 (which is 5 or greater), we round the 1 up to 2. Thus, 1.7 rounds to 2.
  1. Calculating the Estimated Value

Now that we have rounded each value to one significant figure, we substitute these values back into our original expression:

\[ \frac{4 + 8}{2} \]

Next, we calculate the numerator by performing the addition:
\[ 4 + 8 = 12 \]

Finally, we perform the division by the rounded denominator:
\[ \frac{12}{2} = 6 \]

Thus, the estimated value of the expression \(\frac{4.3 + 7.5}{1.7}\) is 6.

Examples

Rounding numbers is a vital skill in daily life, especially when performing quick mental math. For instance, if you are shopping and see items priced at \$\$4.30\$ and \$\$7.50\$, and you need to pay a shared cost divided among \$1.7\$ people (perhaps a partial group), you can quickly round these numbers to get a rough estimate of the total expenditure, helping you manage your budget on the go without needing a calculator for exact results. This method simplifies complex expressions into easily manageable mental figures.

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