What is 0.208 as a fraction?

In this article, we will guide you step by step through the process of converting the decimal 0.208 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 0.208 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.

0.208 as a fraction equals 208/1000 or 26/125

Now let's break down the steps for converting 0.208 into a fraction.

Step 1:

First, we express 0.208 as a fraction by placing it over 1:
0.208/1

Step 2:

Next, we multiply both the numerator and denominator by 10 for each digit after the decimal point.
0.208 x 1000/1 x 1000
  =  
208/1000

Step 3:

Next, we find the Greatest Common Factor (GCF) for 208 and 1000. Keep in mind a factor is just a number that divides into another number without any remainder.
The factors of 208 are: 1 2 4 8 13 16 26 52 104 208
The factors of 1000 are: 1 2 4 5 8 10 20 25 40 50 100 125 200 250 500 1000
The GCF of 208 and 1000 is: 8

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 8 in this case.
208 ÷ 8/1000 ÷ 8
  =  
26/125


Great Work! We've just determined that 0.208 as a fraction equals 208/1000 or 26/125 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 does the Greatest Common Factor (GCF) mean?

The greatest common factor is also referred to as the highest common factor. In math, this refers to the greatest common divisor of two or more whole numbers (also known as integers). In simple terms, this is the biggest number that can divide evenly into two or more numbers. For example, the GCF for 4 and 8 is 4.

What is the Least Common Multiple (LCM)?

The Least Common Multiple (LCM) of two or more numbers is the smallest number that is a multiple of each of the given numbers. For example, the LCM of 4 and 6 is 12.

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.

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 as a percentage?

A decimal can be converted to a percentage by multiplying it by 100 and adding a percent sign. For example, 0.75 × 100 = 75%.


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.

Build math skills with Brilliant.org interactive problem solving puzzles designed for adults. Algebra, geometry, logic, and probability are covered with video guides.

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

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



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