Lesson Description
In this lesson, you will learn how to convert fractions into decimals and decimals into fractions. Understanding place value and division is key to mastering these conversions.
Learning Objectives
- Convert fractions to terminating decimals using division.
- Convert decimals to fractions using place value.
- Simplify fractional answers.
Topics Covered
- Long division with decimals
- Place value review
- Simplifying fractions
Key Terms
- Decimal: A number written using a decimal point to show fractional parts of ten.
- Terminating Decimal: A decimal that ends.
- Repeating Decimal: A decimal with digits that repeat forever.
Lesson Examples
Example 1: Convert 3/4 to a Decimal
- Divide 3 by 4.
- 3 ÷ 4 = 0.75.
- Answer: 0.75
Example 2: Convert 1/5 to a Decimal
- Divide 1 by 5.
- 1 ÷ 5 = 0.2.
- Answer: 0.2
Example 3: Convert 0.6 to a Fraction
- 0.6 means 6 tenths → 6/10.
- Simplify 6/10 to 3/5.
- Answer: 3/5
Example 4: Convert 0.125 to a Fraction
- 0.125 = 125/1000.
- Simplify by dividing numerator and denominator by 125.
- 125/1000 = 1/8.
- Answer: 1/8
Practice Problems
- Convert 2/5 to a decimal.
- Convert 7/8 to a decimal.
- Convert 0.4 to a fraction.
- Convert 0.75 to a fraction.
- Convert 0.05 to a fraction and simplify.
Tips & Common Mistakes
- Remember that dividing the numerator by the denominator gives the decimal.
- Use place value to write decimals as fractions.
- Always simplify fractions to lowest terms.
Summary
Fractions and decimals represent the same values in different forms. Converting between them requires division and understanding place value. Mastery of these skills builds a strong foundation for working with percents in the next lesson.
Challenge Problems
- Convert 5/16 to a decimal.
- Convert 0.375 to a fraction and simplify.
- Explain why some fractions produce repeating decimals.