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# 0.123 as a Fraction

Here you can find 0.123 as a fraction, both as decimal fraction and in simplest form as displayed in our converter right below 🙂

Decimal:
Fraction:
123/1000

## How to Convert 0.123 to Decimal?

Now we show you how to change the number using the step by step instructions which can be found on our home page.

0.123 has 3 decimal places, so we put the decimal digits of 0.123, 123, over 1 followed by the number of zeroes equal to the number of decimal places, 3: 123 = 123/1000.

0.123 as decimal fraction = 123/1000

123 is the nominator and 1000 is the denominator.

We now check if our result is already in the lowest terms by finding the greatest common factor of 123 and 1000, know as gcf of 123 and 1000.

The gcf(123,1000) is 1, so we can conclude that 123/1000 already is in simplest form. We write it as 123/1000.

0.123 as a fraction in its lowest terms is 123/1000

## What is 0.123 as a Fraction?

We have already answered the question for the case decimal fraction in simplest form.

Yet, by multiplying the denominator and the nominator of our result in simplest form with all integers distinct from zero and one we can generate an infinite amount of fractions equivalent to 123/1000, but not in lowest terms:

123/1000 = .

For example, with n = 2 we obtain 246/2000 and with n = -3 we get 369/3000:
246/2000 = 369/3000 = 123/1000.

We can thus conclude that the question under consideration does not have a single answer, but an indefinite amount of possibilities.

## 0.123 Repeating as a Fraction

To find out what is 0.123… as a fraction, identify the repeating sequence or pattern, known as reptend or repetend of 0.123 recurring.

The infinitely-repeated digit sequence of 0.123… can be indicated by three periods.

For example, 0.12333… as a fraction (repeating 3, the last digit) = 37/300.

Alternatively, a vinculum, that is a horizontal line, can be drawn above the repetend of the fraction of 0.123. In addition, one can sometimes see the period enclosed in parentheses ().

Here, we use the overlined notation to denote 0.123 repeating as a fraction:

0.123 = 37/300
0.123 = 61/495
0.123 = 41/333

These results for 0.123 repeating as a fraction are approximations and limited to three digits fractions.

For different periods, higher precision and more results use the calculator below.

BTW: Our app changes a number such as 0.123 on the fly, just make sure to enter enough decimal digits in case your number contains repeating decimal places.

You certainly know what the decimal 0.123 in numerator / denominator notation is.

This brings us the end of our article.

## Summary

We are left with classifying 0.123 as rational number because in can be written as 123/1000; 123 and 1000 are integers.

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– Article written by Mark