What is 13/4 as a decimal?

Understand the Problem

The question asks us to convert the fraction 13/4 into its decimal form. This involves dividing the numerator (13) by the denominator (4).

Answer

The decimal form of $ \frac{13}{4} $ is $ 3.25 $.

Steps to Solve

Setup the Division Begin by setting up the division of 13 by 4. This involves the format where 13 is divided by 4: $$ 13 \div 4 $$
Perform the Division Calculate how many times 4 fits into 13. The whole number part is 3 because: $$ 4 \times 3 = 12 $$ This indicates that 4 fits into 13 three times.
Calculate the Remainder After subtracting 12 from 13, we find the remainder: $$ 13 - 12 = 1 $$
Add Decimal Points Next, we express the remainder as a fraction by adding a decimal point to the 13 and bringing down a zero, making it 10 (this represents the 0.1 in the decimal): $$ 10 \div 4 $$
Perform the Next Division Now divide 10 by 4, which fits 2 times: $$ 4 \times 2 = 8 $$
Calculate the New Remainder Subtract 8 from 10: $$ 10 - 8 = 2 $$
Add Another Decimal Point Again, add another zero to make it 20, then divide: $$ 20 \div 4 $$
Final Division This fits 5 times: $$ 4 \times 5 = 20 $$
Conclusion After subtracting again: $$ 20 - 20 = 0 $$

This indicates that the decimal division is complete.

The decimal form of the fraction ( \frac{13}{4} ) is ( 3.25 ).

More Information

The decimal ( 3.25 ) can be understood as 3 whole parts and an additional 0.25, which is equal to ( \frac{1}{4} ) in fraction form. This type of conversion is common in math, linking fractions and decimals together.

Tips

Misplacing the decimal point during the division. Always ensure to correctly track how many times the divisor fits into the numerator, especially after adding decimal points.
Forgetting to bring down the next digit when necessary. Be attentive to how you handle remainders and conversion to decimals.

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