What is 13/4 as a decimal?
Understand the Problem
The question is asking for the decimal representation of the fraction 13/4. To convert it, we divide 13 by 4.
Answer
The decimal representation of $\frac{13}{4}$ is $3.25$.
Answer for screen readers
The decimal representation of the fraction $\frac{13}{4}$ is $3.25$.
Steps to Solve
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Set Up the Division We need to perform the division of 13 by 4 to find the decimal representation.
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Perform the Division Carry out the division: $$ 13 \div 4 $$
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Calculate the Quotient When you divide, you get: $$ 4 \text{ (the whole number part)} $$ This is because 4 fits into 13 three times.
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Calculate the Remainder Subtract $4 \times 3 = 12$ from 13 to find the remainder: $$ 13 - 12 = 1 $$
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Express the Remainder as a Decimal Now, take the remainder and continue the division by adding a decimal point and a zero. Thus: $$ 10 \div 4 = 2 $$ So the next digit is 2.
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Calculate the New Remainder Now calculate: $$ 10 - (4 \times 2) = 10 - 8 = 2 $$
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Repeat for Decimal Expansion Continue this process with the remainder: $$ 20 \div 4 = 5 $$ And find: $$ 20 - (4 \times 5) = 0 $$
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Compile the Results Putting it all together, you have: $$ 13 \div 4 = 3.25 $$
The decimal representation of the fraction $\frac{13}{4}$ is $3.25$.
More Information
The division of 13 by 4 results in a decimal of 3.25, which tells us that there are 3 whole parts and a quarter of another part.
Tips
A common mistake is to forget to add a decimal point when the integer division does not fully fit, or to miscalculate the remainders leading to incorrect digits in the decimal.
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