Convert between place values

Learning Objectives Algebraically represent multi-digit numbers using place value notation. Construct and solve systems of linear equations derived from word problems about digits and place values. Generalize the concept of place value to represent numbers in any base 'b' as a polynomial expression. Formulate and solve equations where the base of a number system is an unknown variable. Analyze the relationship between a number and the number formed by reversing its digits. Apply place value conversion principles to solve problems involving number theory and abstract algebra. If a two-digit number in an unknown base, written as '35', is equal to 26 in our familiar base-10 system, can you find the value of the unknown base? 🤔 This tutorial elevates the el...

TermDefinitionExample Place ValueThe value represented by a digit in a number on the basis of its position. In a base-b system, the rightmost digit is the b^0 place, the next is the b^1 place, and so on.In the number 472 (base-10), the '4' is in the hundreds (10^2) place, the '7' is in the tens (10^1) place, and the '2' is in the ones (10^0) place. Its value is 4*10^2 + 7*10^1 + 2*10^0. Base (Radix)The number of unique digits, including zero, used to represent numbers in a positional numeral system. Base-10 (decimal) uses 10 digits (0-9); base-2 (binary) uses 2 digits (0, 1).The number 1101 in base-2 is equal to 1*2^3 + 1*2^2 + 0*2^1 + 1*2^0 = 8 + 4 + 0 + 1 = 13 in base-10. Polynomial Representation of a NumberExpressing a number as a polynomial where the var...

Algebraic Representation (Base-10) A number with digits d_n d_{n-1} ... d_1 d_0 is represented as: V = d_n \cdot 10^n + d_{n-1} \cdot 10^{n-1} + ... + d_1 \cdot 10^1 + d_0 \cdot 10^0 Use this formula to convert a number described in terms of its digits into a single algebraic expression that can be used in an equation. Algebraic Representation (General Base-b) A number with digits d_n d_{n-1} ... d_1 d_0 in base-b is represented as: V = d_n \cdot b^n + d_{n-1} \cdot b^{n-1} + ... + d_1 \cdot b^1 + d_0 \cdot b^0 This is the generalized form used for problems involving unknown or non-decimal bases. Note that for a number to be valid in base-b, all its digits d_i must satisfy 0 <= d_i < b. Reversed Digits Relationship For a two-digit number 10x+y, the reversed numbe...