Learn on PengiPengi Math (Grade 5)Chapter 1: Palace Value and Powers of 10

Lesson 5: Equivalent, Comparing, and Ordering Decimals

In this Grade 5 lesson from Pengi Math Chapter 1, students learn to recognize and generate equivalent decimals by adding or removing trailing zeros, then compare decimals by aligning decimal points and analyzing place values. Students also practice rewriting decimals using like units and applying place value reasoning to order decimals from least to greatest or greatest to least.

Section 1

Equivalent Decimals

Property

Equivalent decimals are decimals that name the same number or represent the same value. You can create an equivalent decimal by adding or removing zeros at the end of a decimal, to the right of the last non-zero digit.

0.7=0.70=0.7000.7 = 0.70 = 0.700

Section 2

Compare by Aligning Place Values

Property

To compare decimals, align them by their decimal points. Compare the digits in each place value, starting from the largest place (leftmost). The first place where the digits differ determines which number is greater.

Examples

Section 3

Ordering Decimals

Property

Ordering decimals involves arranging a set of numbers from least to greatest (ascending order) or greatest to least (descending order). This is achieved by repeatedly applying pairwise comparison to the numbers in the set.

Examples

Book overview

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Chapter 1: Palace Value and Powers of 10

  1. Lesson 1

    Lesson 1: Extending Place Value to Decimals

  2. Lesson 2

    Lesson 2: Representing Numbers Using Powers of 10

  3. Lesson 3

    Lesson 3: Multiplying and Dividing Whole Numbers by Powers of 10

  4. Lesson 4

    Lesson 4: Representing Decimals in Multiple Forms

  5. Lesson 5Current

    Lesson 5: Equivalent, Comparing, and Ordering Decimals

  6. Lesson 6

    Lesson 6: Rounding Decimals to Any Place

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Equivalent Decimals

Property

Equivalent decimals are decimals that name the same number or represent the same value. You can create an equivalent decimal by adding or removing zeros at the end of a decimal, to the right of the last non-zero digit.

0.7=0.70=0.7000.7 = 0.70 = 0.700

Section 2

Compare by Aligning Place Values

Property

To compare decimals, align them by their decimal points. Compare the digits in each place value, starting from the largest place (leftmost). The first place where the digits differ determines which number is greater.

Examples

Section 3

Ordering Decimals

Property

Ordering decimals involves arranging a set of numbers from least to greatest (ascending order) or greatest to least (descending order). This is achieved by repeatedly applying pairwise comparison to the numbers in the set.

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 1: Palace Value and Powers of 10

  1. Lesson 1

    Lesson 1: Extending Place Value to Decimals

  2. Lesson 2

    Lesson 2: Representing Numbers Using Powers of 10

  3. Lesson 3

    Lesson 3: Multiplying and Dividing Whole Numbers by Powers of 10

  4. Lesson 4

    Lesson 4: Representing Decimals in Multiple Forms

  5. Lesson 5Current

    Lesson 5: Equivalent, Comparing, and Ordering Decimals

  6. Lesson 6

    Lesson 6: Rounding Decimals to Any Place