What is 1.78345 as a fraction?

In this article, we will guide you step by step through the process of converting the decimal 1.78345 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 1.78345 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.

1.78345 as a fraction equals 178345/100000 or 35669/20000

Now let's break down the steps for converting 1.78345 into a fraction.

Step 1:

First, we express 1.78345 as a fraction by placing it over 1:
1.78345/1

Step 2:

Next, we multiply both the numerator and denominator by 10 for each digit after the decimal point.
1.78345 x 100000/1 x 100000
  =  
178345/100000

Step 3:

Next, we find the Greatest Common Factor (GCF) for 178345 and 100000. Keep in mind a factor is just a number that divides into another number without any remainder.
The factors of 178345 are: 1 5 53 265 673 3365 35669 178345
The factors of 100000 are: 1 2 4 5 8 10 16 20 25 32 40 50 80 100 125 160 200 250 400 500 625 800 1000 1250 2000 2500 3125 4000 5000 6250 10000 12500 20000 25000 50000 100000
The GCF of 178345 and 100000 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.
178345 ÷ 5/100000 ÷ 5
  =  
35669/20000


Great Work! We've just determined that 1.78345 as a fraction equals 178345/100000 or 35669/20000 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.

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 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 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%.

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.

Use Study.com for an entertaining video lesson approach.

For fun game based learning try Prodigy Math.

For a UK based curriculum the BBC.co.uk provides a useful classroom aid to math lessons.



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