What is 0.312 as a fraction?

In this article, we will guide you step by step through the process of converting the decimal 0.312 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 0.312 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.

0.312 as a fraction equals 312/1000 or 39/125

Now let's break down the steps for converting 0.312 into a fraction.

Step 1:

First, we express 0.312 as a fraction by placing it over 1:
0.312/1

Step 2:

Next, we multiply both the numerator and denominator by 10 for each digit after the decimal point.
0.312 x 1000/1 x 1000
  =  
312/1000

Step 3:

Next, we find the Greatest Common Factor (GCF) for 312 and 1000. Keep in mind a factor is just a number that divides into another number without any remainder.
The factors of 312 are: 1 2 3 4 6 8 12 13 24 26 39 52 78 104 156 312
The factors of 1000 are: 1 2 4 5 8 10 20 25 40 50 100 125 200 250 500 1000
The GCF of 312 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.
312 ÷ 8/1000 ÷ 8
  =  
39/125


Great Work! We've just determined that 0.312 as a fraction equals 312/1000 or 39/125 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.

Why is there a need to convert decimals to fractions anyway?

The U.S. is one of a few countries worldwide that still uses the Imperial system of measurement, which is a fractional measurement system, where items are measured in feet, inches, pounds, ounces, yards, and so on. The majority of the rest of the world uses the metric system, which is a decimal measurement system, where items are measured in cm, meters, grams, kilos, and so on.

What are composite numbers?

Composite numbers are numbers that are greater than 1 and have more than two factors. For example, 6 is a composite number because it has factors 1, 2,3 and 6.

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 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 ratio?

A ratio is a relationship between two numbers that shows how many times one value is contained within another. For example, the ratio 3:1 means there are 3 parts of one quantity for every 1 part of another.

What is a fraction as a percentage?

A fraction can be converted to a percentage by dividing the numerator by the denominator and multiplying by 100. For example, 3/6 = 1/2 = 0.50 × 100 = 50%.


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.

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

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



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