Roy wants to make a number that rounds to 54.6 when rounded to 1 decimal place. Which four number cards could he use to complete the number in the box?
Understand the Problem
The question is asking us to determine which four number cards can be combined to create a number that rounds to 54.6 when rounded to one decimal place. To solve this, we need to identify numbers between 54.55 and 54.64 inclusive, since those round to 54.6.
Answer
The four number cards are $5$, $4$, $6$, and $6$.
Answer for screen readers
The four number cards Roy can use are 5, 4, 6, and 6.
Steps to Solve
- Identify the Range of Valid Numbers
To round to 54.6, the number must be between 54.55 and 54.64 inclusive.
- Determine Possible Combinations
The available cards are 5, 4, 6, 0, 2, 3, 8. We need to form a four-digit number with these cards that falls into our identified range.
- Explore Possible Combinations
We focus on combinations that start with 54. The fourth digit needs to be either 5, 6, or 0 to satisfy the rounding condition:
- Try with 54X where X could be 5, 6, or 0.
- If X = 5, the number is 54.5
- If X = 6, the number is 54.6
- If X = 0, the number is 54.0
- Formulate Valid Combinations
Using the digits:
- 54.6 (valid combination: 5, 4, 6, 6)
- 54.5 (valid combination: 5, 4, 5, 0)
- 54.8 (but did not use valid cards)
- Select the Correct Four Cards
After checking the combinations that round to 54.6:
- The valid cards used are 5, 4, 6, and 6.
The four number cards Roy can use are 5, 4, 6, and 6.
More Information
The number 54.6 rounds to 54.6 when rounded to one decimal place. The combination of cards must create a number within the specified range, ensuring the last digit aligns correctly.
Tips
- Misunderstanding the rounding rules, especially thinking that certain digit placements do not affect the rounding outcome.
- Incorrectly assuming combinations without considering the complete number formed.
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