Question

If $a$, $b$, $c$, and $d$ are four different digits from $1$ to $9$, inclusive, then what's the largest possible value for the decimal $a.b + c.d$ ?

Answer 1

The largest possible value for the decimal a.b + c.d is 9.7 + 8.6, which equals 18.3, given that a, b, c, and d are different digits from 1 to 9.

Step-by-step explanation:

To find the largest possible value for the decimal a.b + c.d, where a, b, c, and d are different digits from 1 to 9, we need to assign the largest digits to the a and c positions since they have a higher place value. Since we're working with decimals, the a and c positions will contribute more to the total than the b and d positions.

Therefore, the largest values we can pick for a and c are 9 and 8, respectively, since we can't reuse digits. For b and d, we should pick the next largest digits, which are 7 and 6. The largest possible value for the decimal is therefore 9.7 + 8.6, which equals 18.3.