Write 55/12 as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.

Steps to Solve

1. Perform the Division To convert the fraction $\frac{55}{12}$ into decimal form, we need to perform the division of 55 by 12.

2. Calculate Whole Number Part When we divide, we first find how many times 12 fits into 55. $$ 55 \div 12 = 4 \text{ (whole number part)} $$

3. Calculate the Remainder After subtracting, we find the remainder. $$ 55 - (12 \times 4) = 55 - 48 = 7 $$

4. Perform Long Division for Decimal Now, we add a decimal point and continue the division by adding zeroes to the remainder. We bring down a zero (making it 70) and divide again. $$ 70 \div 12 = 5 \text{ (next digit)} $$

5. Find New Remainder Now, we calculate the new remainder. $$ 70 - (12 \times 5) = 70 - 60 = 10 $$

6. Continue Long Division Again, we bring down a zero (making it 100) and divide. $$ 100 \div 12 = 8 \text{ (next digit)} $$

7. Calculate Next Remainder Calculate the remainder once more. $$ 100 - (12 \times 8) = 100 - 96 = 4 $$

8. Repeat Process Bringing down another zero (making it 40) and divide again. $$ 40 \div 12 = 3 \text{ (next digit)} $$

9. Calculate New Remainder Again $$ 40 - (12 \times 3) = 40 - 36 = 4 $$

Now, we notice that the remainder returns to 4, meaning the digits will repeat.

10. Final Decimal Representation The repeating digits are "3", so we can write the decimal as: $$ 4.58333... = 4.58\overline{3} $$