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

Lesson 1: Extending Place Value to Decimals

In this Grade 5 lesson from Pengi Math Chapter 1, students extend the place value system beyond whole numbers to include tenths, hundredths, and thousandths. They learn that each place to the right is one-tenth the value of the place to its left, and practice interpreting decimals as fractions with denominators of 10, 100, and 1,000. Students also develop precise unit language to describe decimal values accurately.

Section 1

Extending Place Value to Thousandths

Property

Dividing a place value unit by 10 results in the next smaller unit to its right. This pattern extends the place value chart to include decimals such as tenths, hundredths, and thousandths.

1 hundredth÷10=1 thousandth1 \text{ hundredth} \div 10 = 1 \text{ thousandth}
0.01×110=0.0010.01 \times \frac{1}{10} = 0.001

Examples

  • 1000000×110=1000001000000 \times \frac{1}{10} = 100000 (one million ÷ 10 = one hundred thousand)
  • 100000×110=10000100000 \times \frac{1}{10} = 10000 (one hundred thousand ÷ 10 = ten thousand)
  • 10000×110=100010000 \times \frac{1}{10} = 1000 (ten thousand ÷ 10 = one thousand)
  • 1×110=0.11 \times \frac{1}{10} = 0.1 (one ÷ 10 = one tenth)
  • 0.1×110=0.010.1 \times \frac{1}{10} = 0.01 (one tenth ÷ 10 = one hundredth)
  • 0.01×110=0.0010.01 \times \frac{1}{10} = 0.001 (one hundredth ÷ 10 = one thousandth)

Section 2

Conceptual Model: Relating Adjacent Place Value Units

Property

Each place value unit is 10 times greater than the unit to its immediate right.
This creates a multiplicative relationship where one of a larger unit can be decomposed into ten of the next smaller unit.

1 one=10 tenths1 \text{ one} = 10 \text{ tenths}
1 tenth=10 hundredths1 \text{ tenth} = 10 \text{ hundredths}
1 one=100 hundredths1 \text{ one} = 100 \text{ hundredths}

Examples

Book overview

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Chapter 1: Palace Value and Powers of 10

  1. Lesson 1Current

    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 5

    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.

Expand

Section 1

Extending Place Value to Thousandths

Property

Dividing a place value unit by 10 results in the next smaller unit to its right. This pattern extends the place value chart to include decimals such as tenths, hundredths, and thousandths.

1 hundredth÷10=1 thousandth1 \text{ hundredth} \div 10 = 1 \text{ thousandth}
0.01×110=0.0010.01 \times \frac{1}{10} = 0.001

Examples

  • 1000000×110=1000001000000 \times \frac{1}{10} = 100000 (one million ÷ 10 = one hundred thousand)
  • 100000×110=10000100000 \times \frac{1}{10} = 10000 (one hundred thousand ÷ 10 = ten thousand)
  • 10000×110=100010000 \times \frac{1}{10} = 1000 (ten thousand ÷ 10 = one thousand)
  • 1×110=0.11 \times \frac{1}{10} = 0.1 (one ÷ 10 = one tenth)
  • 0.1×110=0.010.1 \times \frac{1}{10} = 0.01 (one tenth ÷ 10 = one hundredth)
  • 0.01×110=0.0010.01 \times \frac{1}{10} = 0.001 (one hundredth ÷ 10 = one thousandth)

Section 2

Conceptual Model: Relating Adjacent Place Value Units

Property

Each place value unit is 10 times greater than the unit to its immediate right.
This creates a multiplicative relationship where one of a larger unit can be decomposed into ten of the next smaller unit.

1 one=10 tenths1 \text{ one} = 10 \text{ tenths}
1 tenth=10 hundredths1 \text{ tenth} = 10 \text{ hundredths}
1 one=100 hundredths1 \text{ one} = 100 \text{ hundredths}

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 1Current

    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 5

    Lesson 5: Equivalent, Comparing, and Ordering Decimals

  6. Lesson 6

    Lesson 6: Rounding Decimals to Any Place