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 prime numbers?

Prime numbers are numbers greater than 1 that have only two factors: 1 and themselves. Examples include 2, 3, 5, 7, 11, 13, 17 and so on.

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 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 a proportion?

A proportion is an equation that states that two ratios are equal. For example, 1/2 = 2/4 shows a proportional relationship.

What is a mean (average)?

The mean, or average, is calculated by adding all the numbers in a set and dividing by the total number of values. For example, the mean of 3, 4, and 5 is (3 + 4 + 5)/3 = 4.

What is a decimal place?

A decimal place refers to the position of a digit to the right of the decimal point. For example, in 3.141, the digit 1 is in the thousandths place.


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.

Use Study.com for an entertaining video lesson approach.

For personalized 1-1 lessons check out Preply.com.

For early learners we recommend IXL Math. The math courses range from Pre-K to grade 12.



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