What is 0.845 as a fraction?

In this article, we will guide you step by step through the process of converting the decimal 0.845 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 0.845 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.

0.845 as a fraction equals 845/1000 or 169/200

Now let's break down the steps for converting 0.845 into a fraction.

Step 1:

First, we express 0.845 as a fraction by placing it over 1:
0.845/1

Step 2:

Next, we multiply both the numerator and denominator by 10 for each digit after the decimal point.
0.845 x 1000/1 x 1000
  =  
845/1000

Step 3:

Next, we find the Greatest Common Factor (GCF) for 845 and 1000. Keep in mind a factor is just a number that divides into another number without any remainder.
The factors of 845 are: 1 5 13 65 169 845
The factors of 1000 are: 1 2 4 5 8 10 20 25 40 50 100 125 200 250 500 1000
The GCF of 845 and 1000 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.
845 ÷ 5/1000 ÷ 5
  =  
169/200


Great Work! We've just determined that 0.845 as a fraction equals 845/1000 or 169/200 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.

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 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 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 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.


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 early learners we recommend IXL Math. The math courses range from Pre-K to grade 12.

Desmos.com has a focus on equation, functions and visual graphs.

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



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