What is 0.205 as a fraction?

In this article, we will guide you step by step through the process of converting the decimal 0.205 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 0.205 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.

0.205 as a fraction equals 205/1000 or 41/200

Now let's break down the steps for converting 0.205 into a fraction.

Step 1:

First, we express 0.205 as a fraction by placing it over 1:
0.205/1

Step 2:

Next, we multiply both the numerator and denominator by 10 for each digit after the decimal point.
0.205 x 1000/1 x 1000
  =  
205/1000

Step 3:

Next, we find the Greatest Common Factor (GCF) for 205 and 1000. Keep in mind a factor is just a number that divides into another number without any remainder.
The factors of 205 are: 1 5 41 205
The factors of 1000 are: 1 2 4 5 8 10 20 25 40 50 100 125 200 250 500 1000
The GCF of 205 and 1000 is: 5

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 5 in this case.
205 ÷ 5/1000 ÷ 5
  =  
41/200


Great Work! We've just determined that 0.205 as a fraction equals 205/1000 or 41/200 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 irrational numbers?

An irrational number is a number that cannot be expressed as a fraction of two integers. Examples include π (pi) and √2 (the square root of 2).

What is an exponent?

An exponent refers to the number of times a number (the base) is multiplied by itself. For example, 2³ means 2 × 2 × 2 = 8.

What is a square root?

The square root of a number is a value when multiplied by itself, gives that number. For example, the square root of 9 is 3 because 3 × 3 = 9.

What is a percentage as a fraction?

A percentage can be written as a fraction by placing it over 100 and simplifying. For example, 20% = 20/100 = 1/5.

What is a fraction bar?

A fraction bar is the horizontal line that separates the numerator and denominator in a fraction. It also represents division. For example, in 2/4, the fraction bar means 2 divided by 4.


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 personalized 1-1 lessons check out Preply.com.

Math Planet has customized math courses for high school students.

Tailored for college students Paul's Online Math Notes let's students independent study for their math classes. It's also a free service.



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