Convert between place values

Learning Objectives Identify the value of a digit based on its place in a whole number. Identify the value of a digit based on its place in a decimal number. Convert a number from standard form to expanded form using place values. Convert a number from expanded form to standard form using place values. Explain how the value of a digit changes when it moves one place to the left or right. Multiply and divide numbers by powers of 10 to shift place values. Ever wonder why a '5' in 500 is so much bigger than a '5' in 5? 🤔 It's all about place value! In this lesson, we'll explore how the position of a digit determines its value, and learn how to convert numbers between different place value representations. Understanding this helps us work with lar...

TermDefinitionExample Place ValueThe value of a digit based on its position in a number.In the number 345, the digit '4' is in the tens place, so its value is 40. DigitA single symbol used to write numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).In the number 729, the digits are 7, 2, and 9. Whole NumberNumbers without fractions or decimals (e.g., 0, 1, 2, 3, ...).15, 203, 1000 are all whole numbers. Decimal NumberA number that includes a decimal point, representing parts of a whole.3.14, 0.5, 12.75 are all decimal numbers. Expanded FormWriting a number as the sum of the values of its digits.The expanded form of 345 is 300 + 40 + 5. Standard FormThe usual way of writing numbers using digits.The standard form of 'three hundred forty-five' is 345. Powers of 10Numbers like 10, 100...

Shifting Place Values (Multiplication) Multiplying a number by $10^n$ shifts each digit $n$ places to the left. Use this rule when you want to make a number larger by a power of 10. The decimal point moves to the right by 'n' places. For example, $3.45 \times 10^2 = 345$. Shifting Place Values (Division) Dividing a number by $10^n$ shifts each digit $n$ places to the right. Use this rule when you want to make a number smaller by a power of 10. The decimal point moves to the left by 'n' places. For example, $345 \div 10^2 = 3.45$. Expanded Form (Whole Numbers) $abc = a \times 100 + b \times 10 + c \times 1$ To write a whole number in expanded form, multiply each digit by its corresponding place value (e.g., ones, tens, hundreds) and sum the results...