Yamato wants to make a number that rounds to 43.9 when rounded to 1 decimal place. Which four number cards could he use to complete the number in the box?

Steps to Solve

1. Understand the rounding rule To round to one decimal place, look at the digit in the second decimal place. If it's 5 or greater, round up; if it's less than 5, leave the first decimal place unchanged. Thus, to round to 43.9, the second decimal place needs to be anywhere from 0 to 4 (inclusive).

2. Determine the necessary digits We want to form a number like $43.x$ where $x$ is the first decimal place. To round to 43.9, $x$ has to be 9 when we consider the second decimal place. Therefore, our number should look like $43.89$, $43.90$, or $43.91$.

3. Select digits from the available cards The available digit cards are 1, 2, 5, 8, 3, and 9 (not considering the empty space). We already have 4, 3, 9. We need another card from 0-9 to complete it. The options available are:

• To make 3.9, we can use an 8 (as in 43.89),
• To make 4.0, we can use a 0 (assuming we have 0 represented).

4. Verify rounding examples For example:

• $43.89 \rightarrow 43.9$ (round up),
• $43.90 \rightarrow 43.9$ (remains the same),
• $43.91 \rightarrow 43.9$ (rounds down).

Thus valid compositions can be checked against these scenarios.