- The leading digit of \(5,473\) is \(5\), followed by \(4\), so it rounds to \(5,000\).
- The leading digit of \(2,355\) is \(2\), followed by \(3\), so it rounds to \(2,000\).
- Subtracting the rounded values gives \(5,000 - 2,000 = 3,000\).
- The estimated value is \(\boxed{3000}\).
Explanation
- Understanding the Rounding Strategy
We are tasked with estimating the value of \(5,473 - 2,355\) by rounding each number to its leading digit. Rounding to the leading digit means we identify the first non-zero digit from the left, examine the digit immediately to its right, and decide whether to maintain the leading digit or increase it by one. If the digit to the right is less than 5, we keep the leading digit and replace all subsequent digits with zeros. If the digit to the right is 5 or greater, we increase the leading digit by one and replace all subsequent digits with zeros.
- Rounding 5,473 to its Leading Digit
For the number \(5,473\), the leading digit is \(5\) in the thousands place. The digit to its right is \(4\). Since \(4 < 5\), we round down by keeping the leading digit and replacing the remaining digits with zeros. Thus, \(5,473\) rounded to the leading digit is \(5,000\).
- Rounding 2,355 to its Leading Digit
For the number \(2,355\), the leading digit is \(2\) in the thousands place. The digit to its right is \(3\). Since \(3 < 5\), we round down by keeping the leading digit and replacing the remaining digits with zeros. Thus, \(2,355\) rounded to the leading digit is \(2,000\).
- Estimating the Subtraction Result
Now, we perform the subtraction using the two rounded values: \(5,000 - 2,000\). Subtracting these values, we get \(3,000\). Therefore, the estimate of \(5,473 - 2,355\) by rounding to the leading digit is \(3,000\).
Examples
Estimating with leading digits is a handy skill for quick mental math in everyday life, such as when you are shopping and need to roughly estimate the total cost or difference in price between two items before reaching the checkout. For example, if a jacket costs \$5,473 and a pair of boots costs \$2,355, rounding to their leading digits gives you a quick sense that the price difference is around \$3,000, allowing you to gauge your budget instantly without needing an exact calculator.