Subjects arithmetic

Missing Digits Division

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Missing Digits Division


1. **Stating the problem:** We have a division problem with missing digits represented by squares (□). The divisor is $1\,\square\,\square$, the dividend is $8\,\square\,2 . 9\,\square\,\square$, and the quotient ends with $3$. We need to find the missing digits. 2. **Understanding the division setup:** The division is of the form: $$\frac{8\,\square\,2 . 9\,\square\,\square}{1\,\square\,\square} = \text{quotient ending with } 3$$ 3. **Key observations:** - The divisor is a three-digit number starting with 1. - The dividend is a number with digits and decimals. - The quotient ends with digit 3. 4. **Approach:** - Let the divisor be $D = 1ab$ where $a,b$ are digits. - Let the dividend be $N = 8c2.9de$ where $c,d,e$ are digits. - The quotient $Q$ satisfies $Q = \frac{N}{D}$ and ends with digit 3. 5. **Constraints and reasoning:** - Since the divisor starts with 1, $D$ is between 100 and 199. - The dividend starts with 8, so $N$ is about 8000+ (considering decimal places). - The quotient $Q$ is approximately $\frac{N}{D}$. 6. **Trial and error or algebraic approach:** - Since the problem is incomplete without more data, we cannot determine exact digits. 7. **Conclusion:** - More information or context is needed to solve for the missing digits. **Final answer:** Cannot determine missing digits with given information.