55 Divided by 6 Step-by-Step: Visual Long Division and Proof Breakdown
By Sophia Al-Mansoor
To continue past whole numbers into continuous numerical values, convert the leftover remainder into tenths, hundredths, and thousandths. Place a decimal point directly after the 9 in the quotient and add a decimal point followed by trailing zeros to the dividend, writing it as 55.000.
Bring down the first zero next to the remainder 1, creating the value 10. Ask how many times 6 divides into 10. The answer is 1, because 6 × 1 = 6. Place 1 immediately after the decimal point in the quotient (giving 9.1). Subtract 6 from 10 to leave a new remainder of 4.
Bring down another zero to turn 4 into 40. Determine how many times 6 fits into 40. Since 6 × 6 = 36, place a 6 in the quotient's hundredths place (giving 9.16). Subtract 36 from 40, which once again yields 4.
Notice the loop that forms at this stage. Bringing down another zero creates 40 again, leading to another quotient of 6 and another subtraction of 36. Because the remainder 4 continuously recurs, the digit 6 repeats forever. This generates the repeating decimal 9.1666..., commonly rounded to 9.167 for practical measurement.
| Expression Format | Mathematical Value | Precision Type | Typical Application |
|---|---|---|---|
| Improper Fraction | 55/6 | Exact | Algebraic operations, intermediate steps |
| Mixed Number | 9 1/6 | Exact | Physical measurements, carpentry, cooking |
| Quotient & Remainder | 9 R 1 | Discrete Integer | Computer programming (modulo), packaging units |
| Repeating Decimal | 9.16̄ (9.1666...) | Exact (Infinite) | Theoretical mathematics, scientific modeling |
| Rounded Decimal | 9.17 (or 9.167) | Approximation | Financial calculations, everyday engineering |
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