Writing Decimals in Expanded Form with Fractions
This Grade 4 Eureka Math skill teaches students to write decimal numbers in expanded form using both fraction notation and decimal notation. In fraction form, 378.73 = (3 times 100) + (7 times 10) + (8 times 1) + (7 times 1/10) + (3 times 1/100). In decimal form, the same number is 300 + 70 + 8 + 0.7 + 0.03. Students practice both representations for the same number, connecting fractions and decimals at the place value level. This skill from Chapter 30 of Eureka Math Grade 4 solidifies understanding of decimal place value structure.
Key Concepts
A decimal number can be written in expanded form by showing the sum of the value of each digit. The decimal part can be expressed using either fraction notation or decimal notation.
Fraction Expanded Form: $378.73 = (3 \times 100) + (7 \times 10) + (8 \times 1) + (7 \times \frac{1}{10}) + (3 \times \frac{1}{100})$.
Common Questions
What is the expanded form of 45.62 in fraction notation?
40 + 5 + 6/10 + 2/100. Each decimal digit is written as a product of its digit and its place value fraction.
What is the expanded form of 45.62 in decimal notation?
40 + 5 + 0.6 + 0.02. Each digit is written as a decimal value based on its place.
What is the expanded form of 107.09?
Fraction form: 100 + 7 + 0/10 + 9/100 = 100 + 7 + 9/100. Decimal form: 100 + 7 + 0.09. The 0 in the tenths place is typically omitted in fraction form.
Why are there two forms of decimal expanded form?
Fraction notation shows the place value explicitly as fractions (1/10, 1/100). Decimal notation uses decimal values (0.1, 0.01). Both represent the same structure, connecting fraction and decimal understanding.
How does decimal expanded form connect to whole number expanded form?
The structure is the same: each digit times its place value. For whole numbers the values are 1, 10, 100. For decimal places, the values are 1/10 and 1/100 (or 0.1 and 0.01).