If $x, y, z$ be the digits of a number beginning from the left, the number is

### Concept & Formula The algebraic representation of a number relies on the decimal place value system. Each digit in a number is multiplied by a power of 10 corresponding to its position (units, tens, hundreds). ### Step-by-Step Solution **Given:** * The digits of a three-digit number, reading from left to right, are $x$, $y$, and $z$. **Calculation / Deduction:** In a standard base-10 number system, the positions from right to left are units ($10^0$), tens ($10^1$), hundreds ($10^2$), and so on. Because the sequence $x, y, z$ begins from the left, the positions are assigned as follows: * $x$ is in the hundreds place. * $y$ is in the tens place. * $z$ is in the units (ones) place. To find the mathematical value of the number, multiply each digit by its respective place value and sum them up: $\text{Value} = (x \times 100) + (y \times 10) + (z \times 1)$ $\text{Value} = 100x + 10y + z$ ### Exam Strategy & Shortcut Whenever translating digits into algebraic values, strictly map them to standard place values ($1, 10, 100$). A left-to-right reading of a 3-digit number universally translates to $100(\text{first}) + 10(\text{second}) + 1(\text{third})$. Match this structure immediately to option (d). ### Common Pitfall The most common trap is selecting $xyz$. In arithmetic, placing digits next to each other forms a number (like $456$), but in algebra, placing variables next to each other indicates multiplication ($x \times y \times z$). $xyz$ is the product of the digits, not the value of the number itself. ### Final Answer Therefore, the correct answer is **$100x + 10y + z$**.