What is 0.684 as a fraction?

In this article, we will guide you step by step through the process of converting the decimal 0.684 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 0.684 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.

0.684 as a fraction equals 684/1000 or 171/250

Now let's break down the steps for converting 0.684 into a fraction.

Step 1:

First, we express 0.684 as a fraction by placing it over 1:
0.684/1

Step 2:

Next, we multiply both the numerator and denominator by 10 for each digit after the decimal point.
0.684 x 1000/1 x 1000
  =  
684/1000

Step 3:

Next, we find the Greatest Common Factor (GCF) for 684 and 1000. Keep in mind a factor is just a number that divides into another number without any remainder.
The factors of 684 are: 1 2 3 4 6 9 12 18 19 36 38 57 76 114 171 228 342 684
The factors of 1000 are: 1 2 4 5 8 10 20 25 40 50 100 125 200 250 500 1000
The GCF of 684 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.
684 ÷ 4/1000 ÷ 4
  =  
171/250


Great Work! We've just determined that 0.684 as a fraction equals 684/1000 or 171/250 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.

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 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 decimal to a fraction?

To convert a decimal to a fraction, write the decimal as a fraction with a denominator of 10, 100, or 1000 depending on the decimal places, then simplify. For example, 0.75 = 75/100 = 3/4 Reference our decimal to fraction converter page for a detailed breakdown..

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%.

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.

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

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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