Fractions into Decimals Worksheet (with Printable)

Introduction

Mastering the conversion of fractions into decimals is a crucial skill in mathematics. This worksheet provides a comprehensive guide to transform any fraction into its decimal equivalent, empowering you with the confidence to tackle real-world computations.

Understanding Fractions and Decimals

• Fractions: Represent a part of a whole and are expressed in the form a/b, where 'a' is the numerator (the top number) and 'b' is the denominator (the bottom number).
• Decimals: Are another way of expressing numbers as a series of digits to the right of a decimal point. Decimals represent parts of a whole with a denominator of 10, 100, 1,000, and so on.

Conversion Methods

Method 1: Long Division

1. Divide the numerator (a) by the denominator (b).
2. Place the decimal point in the quotient (answer) directly above the decimal point in the dividend.
3. Bring down zeros as needed to continue the division until the remainder is zero or until the desired accuracy is achieved.

Example 1: Convert 1/2 to a decimal.

    0.5
2 | 1.0
   -1  0
      0

Method 2: Multiplication by a Power of 10

1. Multiply the numerator and denominator of the fraction by the same power of 10 until the denominator becomes a whole number.
2. The resulting fraction will have the same value as the original fraction.
3. Convert the whole number denominator to a decimal.

Example 2: Convert 3/4 to a decimal.

3/4 = 3/4 × 10/10
    = 30/40
    = 30 ÷ 40
    = 0.75

Method 3: Using Equivalent Fractions

1. Find an equivalent fraction with a denominator of 10, 100, 1,000, and so on.
2. The numerator of the equivalent fraction will be the decimal equivalent of the original fraction.

Example 3: Convert 5/8 to a decimal.

5/8 = 5/8 × 25/25
    = 125/200
    = 0.625

Worksheet Exercises

Section 1: Basic Conversions

Convert the following fractions to decimals:

1. 1/2
2. 3/4
3. 2/5
4. 7/8
5. 9/10

Section 2: Advanced Conversions

Convert the following improper fractions to decimals:

1. 5/3
2. 7/2
3. 11/4
4. 13/5
5. 17/6

Section 3: Word Problems

1. A pizza is cut into 12 equal slices. If you eat 3 slices, what fraction of the pizza have you eaten? What is this fraction as a decimal?
2. A store is offering a 25% discount on all items. If a shirt originally costs $20, how much will it cost after the discount?

Answer Key

Section 1:

1. 0.5
2. 0.75
3. 0.4
4. 0.875
5. 0.9

Section 2:

1. 1.6666... (rounded to 1.67)
2. 3.5
3. 2.75
4. 2.6
5. 2.8333... (rounded to 2.83)

Answer Key - Word Problems:

1. 3/12 = 0.25
2. 25% of $20 = $20 × 0.25 = $5 (New price = $20 - $5 = $15)

Applications

Converting fractions to decimals has numerous applications in real-world scenarios, including:

• Currency conversions
• Measurement conversions
• Calculating percentages
• Solving equations
• Programming and computer science

Tips and Tricks

• Practice regularly to improve your conversion skills.
• Use a calculator to verify your answers.
• Remember to add zeros when dividing if the remainder is not zero.
• For fractions greater than 1 (improper fractions), convert them to mixed numbers before converting to decimals.

Conclusion

Mastering the conversion of fractions to decimals is an essential mathematical skill that empowers you to tackle a wide range of computations confidently. By understanding the methods and practicing regularly, you can become proficient in this fundamental operation. The provided worksheet and exercises will guide you towards achieving this proficiency.

Printable Worksheet

Download Fractions into Decimals Worksheet