Lesson 2: Converting Decimals
In this lesson, students will understand key features of decimals and how to convert them to equivalent fractions and percentages.
STANDARDS (CCSS & NCTM)
- Grade 7: Multi-Step Real-Life Problems With Decimals, Fractions, and Whole Numbers (CCSS 7.EE.B.3)
- Grade 6–8: Constructing an Argument, Modeling, Using Appropriate Tools, Attending to Precision (CCSS MP3–6); NCTM Number and Operations
- Download a comprehensive Standards Chart (PDF)
Students will be able to:
- Convert decimals to equivalent fractions and percentages; and
- Apply place value concepts to decimals.
- Printable Worksheet 2: "Rock to the Top With Decimals" (PDF) or whiteboard-friendly version
- Printable Bonus Worksheet 2: "Driving With Decimals/Mapping With Proportions" (PDF)
- Worksheet Answer Key (PDF)
Time required: 20 minutes, plus additional time for worksheet(s)
- Ask students where they see decimals in everyday life. Examples might include money ($1.37), sports statistics (4.7 yards per carry), measurement (1.5 gallons), etc.
- Tell students that understanding the place value of decimals will help students better use these numbers in situations both outside of school (like the examples above) and in the classroom. Write a number on the board with four digits to the left of the decimal place and four digits to the right, such as 1,234.5678. Review the values of the places to the left of the decimal point, i.e., the value of the 1 is 1,000 because the digit 1 is in the thousands place, the value of the 2 is 200 because the digit 2 is in the hundreds place, and so on.
- Point out the value of digits to the right of the decimal point, i.e., the 5 is in the tenths place, the 6 is in the hundredths place, the 7 is in the thousandths place, and the 8 is in the ten-thousandths place. Highlight that the place values to the right of a decimal point end in the suffix -th (plural -ths). While the whole number "one hundred" means 100 wholes, the decimal "one hundredth" indicates 1 part out of 100 equal parts (e.g., 1 out of 100 parts of a dollar, or 1 cent).
- Write the following decimals on the board: 0.4, 0.57, and 0.125. Say the name of each decimal, i.e., four tenths, fifty-seven hundredths, and one hundred twenty-five thousandths. Point out how the name of each decimal tells us how to convert them to fractions: 0.4 = 4/10, 0.57 = 57/100, and 0.125 = 125/1,000.
- Point out that some of these fractions can be expressed in simplest terms: 4/10 = 2/5 and 125/1,000 = 1/8.
- Remind students that certain fractions do not convert into simple decimals. For example, 1/3 becomes 0.3 because that is the result of dividing 1 by 3.
- The term percent means “out of 100,” so to convert a decimal to a percentage, multiply the decimal by 100. This will always result in moving the decimal point two places to the right. Then add the percentage symbol. For example, 0.47 = 47%, 0.6 = 60%, and 0.375 = 37.5%.
- Guided Practice: Group students into pairs and ask them to convert the decimals 0.8, 0.14, and 0.002 to fractions and percentages. Then review answers with the class.
[Answers: 0.8 = 8/10 (4/5 expressed in simplest terms) = 80%
0.14 = 14/100 (7/50 expressed in simplest terms) = 14%
0.002 = 2/1000 (1/500 in simplest terms = 0.2%.]
- Independent Practice: Distribute Printable Printable Worksheet 2: "Rock to the Top With Decimals" (PDF) for classwork or homework.
- Check for Understanding: Review worksheet answers with the class using the Worksheet Answer Key (PDF). Have students read their answers aloud. Hearing decimals read aloud reinforces how they convert into fractions.