To estimate the product of \(4,012 \times 19\) by rounding, we will follow a detailed step-by-step solution:
1. Round each number to a convenient place value:
- The first number is \(4,012\). We round \(4,012\) to the nearest thousand.
- Looking at \(4,012\), we see that the value is closest to \(4,000\) since the hundreds digit (0) is less than 5.
- Therefore, \(4,012\) rounded to the nearest thousand is \(4,000\).
- The second number is \(19\). We round \(19\) to the nearest ten.
- Looking at \(19\), it is closest to \(20\) since the units digit (9) is 5 or greater.
- Thus, \(19\) rounded to the nearest ten is \(20\).
2. Calculate the estimated product using the rounded numbers:
- Now multiply the rounded numbers together:
[tex]\[
4,000 \times 20
\][/tex]
3. Perform the multiplication:
- Multiply \(4,000\) by \(20\):
[tex]\[
4,000 \times 20 = 80,000
\][/tex]
4. Conclusion:
- The estimated product of \(4,012 \times 19\) by rounding all the way is \(80,000\).
By following these steps, we find that the estimated product is [tex]\(80,000\)[/tex].
