- Round \(0.17\) to the tenths place, resulting in \(0.2\).
- Round \(6.462\) to the ones place, resulting in \(6\).
- Multiply the rounded numbers: \(0.2 \times 6 = 1.2\).
- The final estimated product is \(\boxed{1.2}\).
Explanation
- Analysis of the Problem and Data Identification
To estimate the product of \(0.17\) and \(6.462\), we follow the rule of rounding each factor to its leftmost nonzero digit. This process helps simplify the numbers while maintaining an approximation that represents their general magnitude.
First, let's identify the leftmost nonzero digit of each number:
- For \(0.17\), the leftmost nonzero digit is \(1\), which is in the tenths place.
- For \(6.462\), the leftmost nonzero digit is \(6\), which is in the ones place.
- Rounding 0.17 to the Nearest Tenth
To round \(0.17\) to the nearest tenth, we look at the digit to the right of the tenths place, which is the hundredths place. The digit in the hundredths place is \(7\). Since \(7\) is greater than or equal to \(5\), we round the tenths digit up by adding \(1\) to it.
Therefore, \(0.17\) rounded to the nearest tenth is \(0.2\).
- Rounding 6.462 to the Nearest One
To round \(6.462\) to the nearest one, we look at the digit to the right of the ones place, which is the tenths place. The digit in the tenths place is \(4\). Since \(4\) is less than \(5\), we round down, which means we keep the ones digit as it is.
Therefore, \(6.462\) rounded to the nearest one is \(6\).
- Calculating the Final Estimated Product
Finally, we multiply the two rounded values to obtain the estimation:
\[0.2 \times 6 = 1.2\]
Thus, the estimated product of \(0.17\) and \(6.462\) is \(\boxed{1.2}\).
Examples
In daily life, quick estimations are often more useful than precise calculations. For example, if you are grocery shopping and buying \(6.462\) pounds of apples at \(\$0.17\) per pound, you can quickly estimate the cost by rounding to \(6\) pounds at \(\$0.20\) per pound, yielding a mental estimate of \(\$1.20\). This allows you to check if your budget is sufficient without needing a calculator.