What is 1.7825 as a fraction?

In this article, we will guide you step by step through the process of converting the decimal 1.7825 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 1.7825 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.

1.7825 as a fraction equals 17825/10000 or 713/400

Now let's break down the steps for converting 1.7825 into a fraction.

Step 1:

First, we express 1.7825 as a fraction by placing it over 1:
1.7825/1

Step 2:

Next, we multiply both the numerator and denominator by 10 for each digit after the decimal point.
1.7825 x 10000/1 x 10000
  =  
17825/10000

Step 3:

Next, we find the Greatest Common Factor (GCF) for 17825 and 10000. Keep in mind a factor is just a number that divides into another number without any remainder.
The factors of 17825 are: 1 5 23 25 31 115 155 575 713 775 3565 17825
The factors of 10000 are: 1 2 4 5 8 10 16 20 25 40 50 80 100 125 200 250 400 500 625 1000 1250 2000 2500 5000 10000
The GCF of 17825 and 10000 is: 25

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 25 in this case.
17825 ÷ 25/10000 ÷ 25
  =  
713/400


Great Work! We've just determined that 1.7825 as a fraction equals 17825/10000 or 713/400 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 whole numbers?

Whole numbers are numbers 0, 1, 2, 3, etc. Whole numbers do not have a decimal point or fractional part. Whole numbers are always positive. Negative numbers are not considered whole.

What are mixed numbers?

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

What are proper fractions?

Proper fractions are fractions where the numerator (the top number) is less than the denominator (the bottom number). Example 2/3

What are simple or reduced fractions?

Simple or reduced fractions are fractions whose top number (numerator) and bottom number (denominator) cannot be any smaller, while still being a whole number. That is to say, the number can no longer be divided by any number other than one while still being a whole number. 1/3 is a good example of a fully reduced fraction.

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 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.


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

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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