What is 0.178 as a fraction?

In this article, we will guide you step by step through the process of converting the decimal 0.178 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 0.178 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.

0.178 as a fraction equals 178/1000 or 89/500

Now let's break down the steps for converting 0.178 into a fraction.

Step 1:

First, we express 0.178 as a fraction by placing it over 1:
0.178/1

Step 2:

Next, we multiply both the numerator and denominator by 10 for each digit after the decimal point.
0.178 x 1000/1 x 1000
  =  
178/1000

Step 3:

Next, we find the Greatest Common Factor (GCF) for 178 and 1000. Keep in mind a factor is just a number that divides into another number without any remainder.
The factors of 178 are: 1 2 89 178
The factors of 1000 are: 1 2 4 5 8 10 20 25 40 50 100 125 200 250 500 1000
The GCF of 178 and 1000 is: 2

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 2 in this case.
178 ÷ 2/1000 ÷ 2
  =  
89/500


Great Work! We've just determined that 0.178 as a fraction equals 178/1000 or 89/500 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 mixed numbers?

A mixed number is made up of a whole number and a proper fraction.

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 terminating decimal?

A terminating decimal is a decimal number that has a finite number of digits after the decimal point. For example, 0.35 and 3.5 are terminating decimals.

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.

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.

Cliff Notes is tailored for independent study for the SAT, ACT, GMAT, GRE, and AP exams. It's a free service.



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