Use all the digits 0, 1, 5, and 3 just once to form the greatest decimal with two decimal places, ensuring 0 is not the last digit. Explain your answer.
Understand the Problem
The question asks to construct the largest possible decimal number using the digits 0, 1, 3, and 5 exactly once each, with two decimal places, and with the restriction that 0 cannot be in the last decimal place. We need to determine the order of the digits that yields the largest decimal and explain the reasoning behind it.
Answer
$5.31$
Answer for screen readers
The greatest decimal with two decimal places using the digits 0, 1, 5, and 3 exactly once, where 0 is not in the last decimal place (hundredths place), is $5.31$. The explanation is as follows: To obtain the largest possible number, we put the largest digit, 5, in the ones place. We then put the next largest digit, 3, in the tenths place. Since 0 cannot be in the hundredths place, we put the next largest digit, 1, there, leaving 0 to be unused.
Steps to Solve
- Determine the largest possible whole number part
To maximize the decimal number, we need to put the largest digits in the whole number part. We have digits 0, 1, 3, and 5. The largest digit is 5, so it should be in the ones place. The next largest digit is 3, so the whole number part is 5.
- Place the decimal point
Since we need two decimal places, the decimal point comes after the ones place. So far, we have $5.$
- Determine the largest possible tenths place
We have digits 0, 1, and 3 remaining. To maximize the decimal part, we should place the next largest digit, 3, in the tenths place. So, we have $5.3$.
- Determine the hundredths place, considering the restriction
We have digits 0 and 1 remaining. Since 0 cannot be in the last decimal place (the hundredths place), we must put 1 in the hundredths place. So the number becomes $5.31$.
- Verify the solution
The largest possible decimal number with two decimal places using the digits 0, 1, 3, and 5, with 0 not in the last place, is $5.31$.
The greatest decimal with two decimal places using the digits 0, 1, 5, and 3 exactly once, where 0 is not in the last decimal place (hundredths place), is $5.31$. The explanation is as follows: To obtain the largest possible number, we put the largest digit, 5, in the ones place. We then put the next largest digit, 3, in the tenths place. Since 0 cannot be in the hundredths place, we put the next largest digit, 1, there, leaving 0 to be unused.
More Information
The problem involves understanding place value and constraints to maximize a decimal number. Finding the largest number often involves placing the largest digits in the most significant places while adhering to the given rules.
Tips
A common mistake is to ignore the constraint that 0 cannot be in the last decimal place. Another mistake would be to not put the largest digits at the start, and instead trying to put smaller digits at the start, and only realizing the mistake later on.
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