Verified Answer :

  • Identify the leftmost nonzero digits for both \(0.938\) (which is \(9\) in the tenths place) and \(2.67\) (which is \(2\) in the ones place).
  • Round \(0.938\) to the nearest tenth: \(0.9\).
  • Round \(2.67\) to the nearest whole number: \(3\).
  • Multiply these rounded values to obtain the estimate: \(0.9 \times 3 = \boxed{2.7}\).

Explanation

  1. Problem Analysis and Data Selection

The objective is to estimate the product of \(0.938\) and \(2.67\) by rounding each factor to the place of its leftmost nonzero digit. We will analyze each number independently based on this rule.

  1. Rounding 0.938

For the first number, \(0.938\), the leftmost nonzero digit is \(9\), which is in the tenths place. To round to this position, we look at the digit to its right, which is \(3\). Since \(3 < 5\), we round down by keeping the tenths digit as it is. Thus, the rounded value of \(0.938\) is \(0.9\).

  1. Rounding 2.67

For the second number, \(2.67\), the leftmost nonzero digit is \(2\), which is in the ones place. To round to this position, we look at the digit to its right, which is \(6\). Since \(6 \geq 5\), we round up by increasing the ones digit by \(1\). Thus, the rounded value of \(2.67\) is \(3\).

  1. Calculating the Final Estimate

Finally, we multiply the two rounded values together: \(0.9 \times 3 = 2.7\). Therefore, the estimated product is \(2.7\).

Examples

Rounding to the leftmost nonzero digit is a quick and efficient way to perform mental math estimates in everyday situations. For example, if you are grocery shopping and trying to estimate the total cost of several items, such as three apples that cost \(\$0.938\) each, you could quickly estimate the total by rounding the price to \(\$0.9\) and multiplying by \(3\) to get \(\$2.70\). This helps you keep track of your budget without needing a calculator.

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