Expand Decimal Fractions

Examples, solutions, and lessons to help Grade 5 students learn how to name decimal fractions in expanded, unit, and word forms by applying place value reasoning.

Common Core Standards: 5.NBT.3
New York State Common Core Math Grade 5, Module 1, Lesson 5
Worksheets for Grade 5

The following diagram shows how to name decimal fractions in standard, word, unit, and expanded forms by applying place value reasoning. Scroll down the page for more examples and solutions.

Lesson 5 Problem Set

1. Express one and three hundred twenty-four thousandths as decimal numerals.
2. Express 11.037 in words.
3. Write the number. 57.281, on a place value chart then write it in expanded form using fractions or decimals to express the decimal place value units.
4. Write a decimal for the following. Use a place value chart to help if necessary.
   a. 7 × 10 + 4 × 1 + 6 × (1/10 ) + 9 × (1/100 ) + 2 × (1/1000 )

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Lesson 5 Homework

1. Express as decimal numerals.
   a. Five thousandths
   b. Thirty-five thousandths
   c. Nine and two hundred thirty-five thousandths
2. Express in words.
   a. 0.008
   b. 15.062
   c. 607.409
3. Write the number on a place value chart then write it in expanded form using fractions or decimals to express the decimal place value units.
   a. 27.346
   b. 0.362
   c. 49.564
4. Write a decimal for each of the following. Use a place value chart to help if necessary. a. 3 × 10 + 5 × 1 + 2 × (1/10) + 7 × (1/100) + 6 × (1/1000)
   b. 9 × 100 + 2 × 10 + 3 × 0.1 + 7 × 0.0001
   c. 5 × 1000 + 4 × 100 + 8 × 1 + 6 × (1/100) + 5 × (1/1000)
5. At the beginning of a lesson, a piece of chalk is 2.967 of an inch. At the end of lesson, it’s 2.308 of an inch.
   Write the two amounts in expanded form using fractions.
   a. At the beginning of the lesson:
   b. At the end of the lesson:
6. Mrs. Herman asked the class to write an expanded form for 412.638. Nancy wrote the expanded form using fractions and Charles wrote the expanded form using decimals. Write their responses.

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