What is 31.25 as a fraction?

In this article, we will guide you step by step through the process of converting the decimal 31.25 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 31.25 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.

31.25 as a fraction equals 3125/100 or 125/4

Now let's break down the steps for converting 31.25 into a fraction.

Step 1:

First, we express 31.25 as a fraction by placing it over 1:
31.25/1

Step 2:

Next, we multiply both the numerator and denominator by 10 for each digit after the decimal point.
31.25 x 100/1 x 100
  =  
3125/100

Step 3:

Next, we find the Greatest Common Factor (GCF) for 3125 and 100. Keep in mind a factor is just a number that divides into another number without any remainder.
The factors of 3125 are: 1 5 25 125 625 3125
The factors of 100 are: 1 2 4 5 10 20 25 50 100
The GCF of 3125 and 100 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.
3125 ÷ 25/100 ÷ 25
  =  
125/4


Great Work! We've just determined that 31.25 as a fraction equals 3125/100 or 125/4 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 are improper fractions?

Improper fractions are fractions where the numerator (the top number) is greater than or equal to the denominator (the bottom number). Example 3/2

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 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 are rounding decimals?

Rounding decimals means adjusting a number to a given place value. For example, rounding 3.186 to two decimal places gives 3.19. Note that last digit which is 6 is closer to 10 than 1 so the digit before it which is 8 move up a value to 9.

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.

Use Study.com for an entertaining video lesson approach.

The Art of Problem Solving provides courses tailored for school students including elementary, middle and high school.

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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