Learn on PengiEureka Math, Grade 4Chapter 33: Money Amounts as Decimal Numbers

Lesson 1: Express money amounts given in various forms as decimal numbers.

In this Grade 4 Eureka Math lesson from Chapter 33, students learn to express money amounts — including pennies, dimes, quarters, and combinations of coins — as decimal numbers using dollar notation. Students connect coin values to fractions of a dollar, such as recognizing that 1 dime equals one-tenth of a dollar and writing it as $0.10, and that 1 penny equals one-hundredth of a dollar written as $0.01. The lesson builds on prior knowledge of fractions with tenths and hundredths to help students fluently convert between cent amounts, fractional dollar notation, and decimal form.

Section 1

Expressing Coin Values as Fractions of a Dollar

Property

The value of a coin can be expressed as a fraction of a dollar by using its value in cents as the numerator and 100 as the denominator.

  • 1 penny = 1 cent = 1100\frac{1}{100} of a dollar
  • 1 dime = 10 cents = 10100\frac{10}{100} (or 110\frac{1}{10}) of a dollar
  • 1 quarter = 25 cents = 25100\frac{25}{100} of a dollar

Examples

Section 2

Calculate the Total Value of a Combination of Coins

Property

To find the total value of a group of coins in cents, multiply the quantity of each coin type by its value in cents and then add the results.

  • 1 quarter = 25 cents
  • 1 dime = 10 cents
  • 1 penny = 1 cent

Total Value in Cents = (No. of quarters×25)+(No. of dimes×10)+(No. of pennies×1)(\text{No. of quarters} \times 25) + (\text{No. of dimes} \times 10) + (\text{No. of pennies} \times 1)

Section 3

Convert Cents to Dollars (Amounts Greater Than 100)

Property

To convert a total number of cents greater than 100 to a decimal dollar amount, write the total cents as the numerator of a fraction with a denominator of 100. This improper fraction can be converted to a mixed number, which directly corresponds to the decimal dollar amount.

Total Cents=Total Cents100 dollars \text{Total Cents} = \frac{\text{Total Cents}}{100} \text{ dollars}

Examples

Section 4

Add and Regroup Money Amounts

Property

To add money amounts, add the dollars and cents separately. If the sum of the cents is 100 or more, regroup by converting every 100 cents into 1 dollar.

100 cents=$1.00100 \text{ cents} = \$1.00

Examples

Book overview

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Chapter 33: Money Amounts as Decimal Numbers

  1. Lesson 1Current

    Lesson 1: Express money amounts given in various forms as decimal numbers.

  2. Lesson 2

    Lesson 2: Solve word problems involving money.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Expressing Coin Values as Fractions of a Dollar

Property

The value of a coin can be expressed as a fraction of a dollar by using its value in cents as the numerator and 100 as the denominator.

  • 1 penny = 1 cent = 1100\frac{1}{100} of a dollar
  • 1 dime = 10 cents = 10100\frac{10}{100} (or 110\frac{1}{10}) of a dollar
  • 1 quarter = 25 cents = 25100\frac{25}{100} of a dollar

Examples

Section 2

Calculate the Total Value of a Combination of Coins

Property

To find the total value of a group of coins in cents, multiply the quantity of each coin type by its value in cents and then add the results.

  • 1 quarter = 25 cents
  • 1 dime = 10 cents
  • 1 penny = 1 cent

Total Value in Cents = (No. of quarters×25)+(No. of dimes×10)+(No. of pennies×1)(\text{No. of quarters} \times 25) + (\text{No. of dimes} \times 10) + (\text{No. of pennies} \times 1)

Section 3

Convert Cents to Dollars (Amounts Greater Than 100)

Property

To convert a total number of cents greater than 100 to a decimal dollar amount, write the total cents as the numerator of a fraction with a denominator of 100. This improper fraction can be converted to a mixed number, which directly corresponds to the decimal dollar amount.

Total Cents=Total Cents100 dollars \text{Total Cents} = \frac{\text{Total Cents}}{100} \text{ dollars}

Examples

Section 4

Add and Regroup Money Amounts

Property

To add money amounts, add the dollars and cents separately. If the sum of the cents is 100 or more, regroup by converting every 100 cents into 1 dollar.

100 cents=$1.00100 \text{ cents} = \$1.00

Examples

Book overview

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

Continue this chapter

Chapter 33: Money Amounts as Decimal Numbers

  1. Lesson 1Current

    Lesson 1: Express money amounts given in various forms as decimal numbers.

  2. Lesson 2

    Lesson 2: Solve word problems involving money.