What is 7.80672 as a fraction?

In this article, we will guide you step by step through the process of converting the decimal 7.80672 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 7.80672 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.

7.80672 as a fraction equals 780672/100000 or 24396/3125

Now let's break down the steps for converting 7.80672 into a fraction.

Step 1:

First, we express 7.80672 as a fraction by placing it over 1:
7.80672/1

Step 2:

Next, we multiply both the numerator and denominator by 10 for each digit after the decimal point.
7.80672 x 100000/1 x 100000
  =  
780672/100000

Step 3:

Next, we find the Greatest Common Factor (GCF) for 780672 and 100000. Keep in mind a factor is just a number that divides into another number without any remainder.
The factors of 780672 are: 1 2 3 4 6 8 12 16 19 24 32 38 48 57 64 76 96 107 114 128 152 192 214 228 304 321 384 428 456 608 642 856 912 1216 1284 1712 1824 2033 2432 2568 3424 3648 4066 5136 6099 6848 7296 8132 10272 12198 13696 16264 20544 24396 32528 41088 48792 65056 97584 130112 195168 260224 390336 780672
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 780672 and 100000 is: 32

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 32 in this case.
780672 ÷ 32/100000 ÷ 32
  =  
24396/3125


Great Work! We've just determined that 7.80672 as a fraction equals 780672/100000 or 24396/3125 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 does the Greatest Common Factor (GCF) mean?

The greatest common factor is also referred to as the highest common factor. In math, this refers to the greatest common divisor of two or more whole numbers (also known as integers). In simple terms, this is the biggest number that can divide evenly into two or more numbers. For example, the GCF for 4 and 8 is 4.

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 is a percentage?

A percentage is a number as a fraction of 100. It is denoted using the '%' symbol. For example, 20% means 20 out of 100.

What is a mean (average)?

The mean, or average, is calculated by adding all the numbers in a set and dividing by the total number of values. For example, the mean of 3, 4, and 5 is (3 + 4 + 5)/3 = 4.

What is a repeating decimal?

A repeating decimal is a decimal in which a digit or group of digits repeats infinitely. For example, 0.3333... (where 3 repeats forever) and 0.142857142857... (where 142857 repeats) are repeating decimals.

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%.


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 a structured learning approach with video lessons try the Khan Academy.

For fun game based learning try Prodigy Math.

For a self-study courses for Algebra. We recommend Purple Math.



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