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?
Understand the Problem
The question is asking which four number cards Yamato could choose to create a number that, when rounded to one decimal place, would be 43.9. To solve this, we need to determine the range of numbers that round to 43.9, which is between 43.85 and 43.94, and identify the relevant digits from the provided cards.
Answer
The digits are 4, 3, 8, and 9. The number formed is $43.89$.
Answer for screen readers
The four number cards that could be used to complete the number are 4, 3, 8, and 9, creating the number 43.89.
Steps to Solve
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Define the range for rounding
We know that to round to 43.9, the number must be between 43.85 and 43.94. This gives us the range:
$$ 43.85 < x < 43.94 $$ -
Extract possible digits for the four cards
The available digits from the cards are: 4, 3, 9, 1, 2, 8, and 5. We need to use four digits to create a number that fits within the specified range. -
Forming the number with available digits
We can form numbers starting with "43" and then check the last two digits. Possible combinations using four digit cards include:- 43.85
- 43.86
- 43.87
- 43.88
- 43.89
- 43.90
- 43.91
- 43.92
- 43.93
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Identify suitable cards for valid combinations
We need to ensure the chosen cards can create a number that falls in the range. Let's check a few valid combinations:- 4 (thousands place)
- 3 (hundreds place)
- Choose two cards from 0, 1, 2, 3, 5, 8, 9 to fill decimal places.
The numbers could be, for example:
- 43.89: uses 4, 3, 8, 9
- 43.90: uses 4, 3, 9, 0
The only achievable combinations are from the existing cards.
The four number cards that could be used to complete the number are 4, 3, 8, and 9, creating the number 43.89.
More Information
The number 43.89 rounds to 43.9 when rounded to one decimal place. This portion of the number, the rounding, allows it to maintain the requirement of being between 43.85 and 43.94.
Tips
- Using numbers outside the available cards: Ensure to only select digits from the provided cards.
- Forgetting that rounding rules apply: Remember that the last digit determines how the number rounds up or down.
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