Represent numbers - up to 10

Learning Objectives Represent integers from 1 to 10 in the binary (base-2) number system. Convert binary numbers back to their decimal (base-10) equivalents. Express the prime factorization of any integer from 1 to 10. Construct a single-variable linear equation for which a given integer from 1 to 10 is the solution. Define and identify triangular numbers within the set {1, 2, ..., 10}. Use set notation to represent subsets of integers from 1 to 10 based on their properties (e.g., prime, even). How can the number 9 be written using only the digits 1 and 0? It's not a trick, it's a different way of thinking about numbers! 🤔 In this tutorial, we will move beyond simple counting to explore advanced ways of representing the familiar numbers 1 through 10. You will lea...

TermDefinitionExample Decimal (Base-10)Our standard number system that uses ten digits (0-9). The position of each digit represents a power of 10.The number 10 is represented as 1×10¹ + 0×10⁰. Binary (Base-2)A number system that uses only two digits (0 and 1). The position of each digit represents a power of 2. A subscript '2' is often used to denote a binary number.The decimal number 5 is written as 101₂ in binary, which means (1 × 2²) + (0 × 2¹) + (1 × 2⁰) = 4 + 0 + 1 = 5. Prime FactorizationThe process of expressing a composite number as the unique product of its prime factors.The prime factorization of 10 is 2 × 5, since 2 and 5 are prime numbers that multiply to 10. Linear EquationAn algebraic equation in which each term is either a constant or the product of a constant and...

Binary to Decimal Conversion N_{10} = d_n \cdot 2^n + d_{n-1} \cdot 2^{n-1} + ... + d_1 \cdot 2^1 + d_0 \cdot 2^0 To convert a binary number to decimal, multiply each binary digit (d) by its corresponding place value (a power of 2) and sum the results. Work from right to left, starting with the 2⁰ (ones) place. Decimal to Binary Conversion (Division Method) N \div 2 = Q_1 \text{ R } r_0; Q_1 \div 2 = Q_2 \text{ R } r_1; ... To convert a decimal number (N) to binary, repeatedly divide the number by 2. Collect the remainders (r) from each division. The binary representation is the sequence of remainders read from the bottom up (last remainder is the first digit). The Fundamental Theorem of Arithmetic N = p_1^{a_1} \cdot p_2^{a_2} \cdot ... \cdot p_k^{a_k} Every integer...