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Fractions To Decimals

Grade 7 Math Worksheets

Introduction

Fractions and decimals are two fundamental concepts in mathematics that often go hand in hand. Understanding how to convert fractions to decimals and vice versa is crucial for many aspects of mathematics, including basic arithmetic, algebra, and even more advanced topics like calculus.

In this guide, we’ll delve into the process of converting fractions to decimals, providing clear explanations and examples to help you master this essential skill.

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Fractions To Decimals - Grade 7 Math Worksheet PDF

This is a free worksheet with practice problems and answers. You can also work on it online.

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What are Fractions and Decimals?

Before we dive into conversions, let’s briefly review what fractions and decimals are:

Fractions

Fractions represent a part of a whole. They consist of a numerator (the top number) and a denominator (the bottom number), separated by a horizontal line. For example, in the fraction 3/4, 3 is the numerator, and 4 is the denominator.

Decimals

Decimals are a way of expressing numbers that are not whole. They include a decimal point, which separates the whole number part from the fractional part. For instance, in the decimal 0.75, 0 is the whole number part, and 75 is the fractional part.

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Converting Fractions to Decimals

Converting fractions to decimals involves dividing the numerator by the denominator. Here’s a step-by-step process:

Step 1: Divide the numerator by the denominator

Perform the division operation. For example, to convert 3/4 to a decimal, divide 3 by 4: 3 ÷ 4 = 0.75.

Step 2: Express the quotient as a decimal

Write down the result you obtained from the division. This is your decimal equivalent of the fraction.

Examples:

Let’s convert a few fractions to decimals using the steps outlined above:

  1. 1/2: Divide 1 by 2: 1 ÷ 2 = 0.5
  2. 3/5: Divide 3 by 5: 3 ÷ 5 = 0.6
  3. 5/8: Divide 5 by 8: 5 ÷ 8 = 0.625

Practice Problems:

Now it’s your turn to try some conversions. Here are a few fractions for you to convert to decimals:

  1. 2/3
  2. 4/7
  3. 7/10

Answer:

  1. 0.66666
  2. 0.574428
  3. 0.7

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Fractions To Decimals FAQS

Why do we need to convert fractions to decimals?

Converting fractions to decimals allows for easier comparison and manipulation of numerical values. Decimals are commonly used in real-world applications, such as in financial calculations, measurements, and scientific notation.

Can all fractions be converted to decimals?

Yes, all fractions can be converted to decimals. However, some fractions may result in repeating or terminating decimals.

What is a terminating decimal?

A terminating decimal is a decimal that ends after a finite number of digits. For example, 0.5 (which is equivalent to 1/2) is a terminating decimal.

What is a repeating decimal?

A repeating decimal is a decimal in which one or more digits repeat infinitely. For example, 0.333… (which is equivalent to 1/3) is a repeating decimal.

How do I know if a fraction will result in a terminating or repeating decimal?

The nature of the decimal expansion depends on the denominator of the fraction. Fractions with denominators that are powers of 2 or powers of 5 will result in terminating decimals. Fractions with denominators that have factors other than 2 or 5 will result in repeating decimals.

Is there a shortcut for converting fractions to decimals?

One shortcut is to recognize common fraction-to-decimal conversions. For example, 1/4 is 0.25, 1/5 is 0.2, and 1/8 is 0.125. Memorizing these common conversions can save time.

How can I convert mixed numbers to decimals?

To convert a mixed number to a decimal, first convert the mixed number to an improper fraction, then follow the steps for converting fractions to decimals as outlined earlier.

Can I convert decimals back to fractions?

Yes, decimals can be converted back to fractions. However, the process may vary depending on whether the decimal is terminating or repeating.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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