What is 0.772 as a fraction?

In this article, we will guide you step by step through the process of converting the decimal 0.772 into a fraction. We will start by understanding how a decimal represents the fractional part of a number, then break down the steps to rewrite 0.772 as a fraction. Finally, we will simplify the fraction by identifying and applying the Greatest Common Factor, ensuring the results are in the simplest form.

By the end of this guide, you should have a good understanding of decimal to fraction conversions and be able to apply this knowledge to various mathematical problems. Let's begin.

0.772 as a fraction equals 772/1000 or 193/250

Now let's break down the steps for converting 0.772 into a fraction.

Step 1:

First, we express 0.772 as a fraction by placing it over 1:
0.772/1

Step 2:

Next, we multiply both the numerator and denominator by 10 for each digit after the decimal point.
0.772 x 1000/1 x 1000
  =  
772/1000

Step 3:

Next, we find the Greatest Common Factor (GCF) for 772 and 1000. Keep in mind a factor is just a number that divides into another number without any remainder.
The factors of 772 are: 1 2 4 193 386 772
The factors of 1000 are: 1 2 4 5 8 10 20 25 40 50 100 125 200 250 500 1000
The GCF of 772 and 1000 is: 4

Step 4:

To simplify the fraction, we divide both the numerator and denominator by their greatest common factor (GCF), which we calculated in the previous step. The GCF value is 4 in this case.
772 ÷ 4/1000 ÷ 4
  =  
193/250


Great Work! We've just determined that 0.772 as a fraction equals 772/1000 or 193/250 in its simplest form.

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Frequently asked math questions, including decimals and fractions

Read the following section to help deepen your understanding of basic math concepts.

What are whole numbers?

Whole numbers are numbers 0, 1, 2, 3, etc. Whole numbers do not have a decimal point or fractional part. Whole numbers are always positive. Negative numbers are not considered whole.

What are improper fractions?

Improper fractions are fractions where the numerator (the top number) is greater than or equal to the denominator (the bottom number). Example 3/2

What are rational numbers?

A rational number is any number that can be expressed as the fraction of two integers, such as 3/4, -5/2, or 0.75.

What is a decimal?

A decimal is a number that includes a decimal point, representing a fraction of a whole. For example, 0.5 represents 1/2.

What is an absolute value?

The absolute value of a number is its distance from zero. For example, the absolute value of -20 is 20.

How do you convert a fraction to a decimal?

A fraction can be converted to a decimal by dividing the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. Check out our fraction page for lots of examples on how to convert fractions into decimals.


Educational math links

There are numerous online resources available (some free and some paid) for learning math including decimals and fractions. These range from interactive games to in-depth courses and lessons. We recommend these websites as a valuable resource for students of all skill levels.

For fun game based learning try Prodigy Math.

Desmos.com has a focus on equation, functions and visual graphs.

For a self-study courses for Algebra. We recommend Purple Math.



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