Estimate 72.51 - 49.264 by first rounding each number to the nearest whole number.
To estimate the difference between \(72.51\) and \(49.264\) by rounding each number to the nearest whole number, we first examine the decimal parts of each value. The rule for rounding to the nearest whole number is as follows: if the first digit after the decimal point is 5 or greater, round the whole number up by adding 1. If the first digit after the decimal point is less than 5, leave the whole number as it is.
For the number \(72.51\), the digit immediately after the decimal point is 5. According to the rounding rule, since this digit is 5, we round up the whole number part. Thus, \(72.51\) rounds up to \(73\). For the number \(49.264\), the digit immediately after the decimal point is 2. Since 2 is less than 5, we round down (or keep) the whole number part. Thus, \(49.264\) rounds down to \(49\).
Now we subtract the rounded number \(49\) from the rounded number \(73\):
\[73 - 49 = 24\]
Therefore, the estimated result of the subtraction \(72.51 - 49.264\) is 24.
Rounding is a practical skill used in everyday situations when an exact value is not required. For example, if you are grocery shopping and have \$72.51, and you need to buy items costing \$49.264, rounding helps you quickly estimate if you have enough money. In this case, estimating \(73 - 49 = 24\) tells you that you will have roughly \$24 left in your pocket. Knowing how to round correctly makes mental math and budgeting much faster and more efficient.