Identify a digit up to the hundreds place

Learning Objectives Define functions using mathematical operators to isolate the ones, tens, and hundreds digits of an integer. Use floor and modulo operations within a functional context to extract specific digits from a number. Evaluate linear, quadratic, and exponential functions where the input variable is a digit extracted from a larger number. Analyze the output of a function to identify a specific digit in the result. Solve problems involving the composition of functions, such as finding f(H(n)) where H(n) is the hundreds digit of n. Apply digit identification functions to solve multi-step problems involving various function types. Ever wonder how a computer program or a digital clock can read just the '7' from the number 742? 💻 It uses a special type of ma...

TermDefinitionExample Digit-Extraction FunctionA function that takes an integer as an input and returns the digit in a specific place value (e.g., ones, tens, or hundreds).If H(n) is the function that finds the hundreds digit, then H(528) = 5. Floor Function: ⌊x⌋The function that takes a real number x as input and returns the greatest integer that is less than or equal to x. It essentially rounds a number down to the nearest whole number.⌊9.81⌋ = 9, and ⌊12.1⌋ = 12. Modulo Operator: modAn operator that finds the remainder after the division of one number by another. It's useful for isolating the last few digits of a number.17 mod 5 = 2, because 17 divided by 5 is 3 with a remainder of 2. Similarly, 123 mod 100 = 23. Function CompositionThe process of applying one function to the resu...

Ones Digit Function: O(n) O(n) = n \mod 10 To find the ones digit of any positive integer n, calculate the remainder when n is divided by 10. This formula effectively isolates the rightmost digit. Tens Digit Function: T(n) T(n) = \lfloor \frac{n \mod 100}{10} \rfloor To find the tens digit, first isolate the last two digits using 'n mod 100'. Then, divide the result by 10 and apply the floor function to remove the decimal part, leaving only the tens digit. Hundreds Digit Function: H(n) H(n) = \lfloor \frac{n \mod 1000}{100} \rfloor To find the hundreds digit, first isolate the last three digits using 'n mod 1000'. Then, divide that result by 100 and apply the floor function to get the hundreds digit.