Convert decimals between standard and expanded form

Learning Objectives Identify the place value of each digit in a decimal number. Define standard form and expanded form of decimal numbers. Convert a decimal from standard form to expanded form using addition. Convert a decimal from standard form to expanded form using multiplication. Convert a decimal from expanded form (addition or multiplication) back to standard form. Explain the value of each digit in a decimal number based on its position. Have you ever wondered how a number like 3.75 can be broken down into its individual parts? 🤔 It's like taking apart a toy to see how it works! In this lesson, you'll learn how to write decimal numbers in two important ways: standard form (the way we usually write them) and expanded form (showing the value of each digit)....

TermDefinitionExample Decimal NumberA number that includes a whole number part and a fractional part, separated by a decimal point.3.14, 0.75, 125.001 Place ValueThe value of a digit based on its position in a number. For decimals, positions to the right of the decimal point represent fractions.In 4.56, the '4' is in the ones place, the '5' is in the tenths place, and the '6' is in the hundredths place. Standard FormThe usual way of writing a number, using digits and a decimal point.The standard form of 'three and twenty-five hundredths' is 3.25. Expanded Form (Addition)A way of writing a number that shows the sum of the values of each digit.The expanded form (addition) of 3.25 is $3 + 0.2 + 0.05$. Expanded Form (Multiplication)A way of writing a nu...

Standard to Expanded Form (Addition) $d_n...d_0.d_{-1}d_{-2}... = (d_n imes 10^n) + ... + (d_0 imes 1) + (d_{-1} imes 0.1) + (d_{-2} imes 0.01) + ...$ To convert a decimal from standard to expanded form using addition, identify the value of each non-zero digit based on its place, and then write these values as a sum. For example, $4.23 = 4 + 0.2 + 0.03$. Standard to Expanded Form (Multiplication) $d_n...d_0.d_{-1}d_{-2}... = (d_n imes 10^n) + ... + (d_0 imes 1) + (d_{-1} imes \frac{1}{10}) + (d_{-2} imes \frac{1}{100}) + ...$ To convert a decimal from standard to expanded form using multiplication, write each non-zero digit multiplied by its place value. Place values for decimals can be written as fractions (e.g., $\frac{1}{10}$, $\frac{1}{100}$) or decimals (e.g., 0...