7/9 In Decimal Form Revealed In 5 Easy Steps

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The mysterious and fascinating world of mathematics has always been a subject of intrigue for many. One of the most enduring and fascinating topics in mathematics is the calculation of pi (π), the ratio of a circle's circumference to its diameter. Among the many intriguing aspects of pi is the calculation of 7/9 in decimal form. In this article, we will delve into the world of mathematics and reveal the calculation of 7/9 in decimal form in 5 easy steps.

Understanding the Basics of Fractions and Decimals

Before we dive into the calculation of 7/9 in decimal form, it is essential to understand the basics of fractions and decimals. A fraction is a way of expressing a part of a whole, and it consists of two parts: the numerator (the top number) and the denominator (the bottom number). A decimal, on the other hand, is a way of expressing a fraction in a form where the denominator is a power of 10.

The Relationship Between Fractions and Decimals

Fractions and decimals are closely related, and it is easy to convert from one to the other. To convert a fraction to a decimal, we simply divide the numerator by the denominator. For example, the fraction 3/4 can be converted to a decimal by dividing 3 by 4, which gives us 0.75.

Step 1: Understanding the Fraction 7/9

The fraction 7/9 is a simple fraction where the numerator is 7 and the denominator is 9. To convert this fraction to a decimal, we need to divide 7 by 9.

Step 2: Dividing 7 by 9

To divide 7 by 9, we can use long division or a calculator. Using long division, we get:

7 ÷ 9 = 0.7777777777777778

As we can see, the result is a repeating decimal, which means that the digits 7 repeat indefinitely.

Step 3: Understanding Repeating Decimals

Repeating decimals are decimals that have a repeating pattern of digits. In the case of 7/9, the repeating pattern is 7. Repeating decimals can be written in a shortened form using a bar over the repeating digits. For example, 0.7777777777777778 can be written as 0.7̄.

Step 4: Converting Repeating Decimals to Finite Decimals

While repeating decimals are a convenient way of expressing fractions, they can be cumbersome to work with. To convert a repeating decimal to a finite decimal, we can use algebraic manipulation. In the case of 7/9, we can multiply both sides of the equation by 10 to get:

10 × 0.7̄ = 7

This equation shows that 0.7̄ is equal to 7/10.

Step 5: Final Calculation

Now that we have converted the repeating decimal to a finite decimal, we can perform the final calculation. Since 7/9 is equal to 0.7̄, which is equal to 7/10, we can write:

7/9 = 0.7777777777777778 ≈ 0.78

And there you have it! The calculation of 7/9 in decimal form is approximately 0.78.