Question

select the equation that shows the estimated difference of the expression below when rounded \\(26.749 - 14.004\\) \\(26.75 - 14.00 = 12.75\\) \\(26.7 - 14.0 = 12.7\\) \\(26.74 - 14.01 = 12.73\\) \\(26.75 - 14.01 = 12.74\\)

Explanation:

Step1: Round the numbers

First, we round \(26.749\) and \(14.004\) appropriately. Rounding \(26.749\) to the nearest hundredth (two decimal places) gives \(26.75\) because the third decimal digit is \(9\), which is more than \(5\), so we round up the second decimal digit. Rounding \(14.004\) to the nearest hundredth gives \(14.00\) because the third decimal digit is \(4\), which is less than \(5\), so we leave the second decimal digit as is.

Step2: Calculate the difference

Now we calculate the difference of the rounded numbers: \(26.75 - 14.00\). Subtracting these, we get \(26.75 - 14.00 = 12.75\).

Answer:

\(26.75 - 14.00 = 12.75\) (the first option)