Convert decimals between standard and expanded form using fractions

Learning Objectives Identify the place value of each digit in a decimal number. Represent decimal digits as fractions based on their place value (tenths, hundredths, thousandths). Convert a decimal in standard form to its expanded form using fractions. Convert a decimal in expanded form (using fractions) to its standard form. Understand the relationship between decimal place values and fractional denominators (10, 100, 1000). Accurately write decimal numbers using fraction notation in expanded form. Have you ever seen a price like $3.75 and wondered what each part really means? 💰 We're going to break down decimals into their fractional pieces! In this lesson, you'll learn how to write decimals in two different ways: standard form (the usual way) and expanded form...

TermDefinitionExample DecimalA number that uses a decimal point to show parts of a whole, where each digit after the decimal point represents a fraction with a denominator of 10, 100, 1000, and so on.3.14, where .14 represents parts of a whole. 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 0.25, the '2' is in the tenths place, and the '5' is in the hundredths place. Standard FormThe usual way of writing a number, using digits and a decimal point if necessary.The standard form of three and twenty-five hundredths is 3.25. Expanded Form (using fractions)Writing a number as the sum of the values of its digits, where the decimal parts are expressed as fractions.The expanded...

Decimal Place Value to Fraction Conversion Rule A digit in the tenths place is represented as $\frac{\text{digit}}{10}$. A digit in the hundredths place is represented as $\frac{\text{digit}}{100}$. A digit in the thousandths place is represented as $\frac{\text{digit}}{1000}$. This rule helps convert each decimal digit into its corresponding fractional value based on its position after the decimal point. The denominator matches the place value (e.g., tenths means 10, hundredths means 100). Standard Form to Expanded Form (using fractions) Rule For a decimal number $W.XYZ...$, its expanded form using fractions is $W + \frac{X}{10} + \frac{Y}{100} + \frac{Z}{1000} + ...$ To convert a decimal to expanded form, first write the whole number part. Then, for each digit after the de...