What is the denominator of 1502 as a repeating decimal? (Recurring digits of 1/1502)

Denominator of 1502 as a repeating decimal

What is the denominator of 1502 as a repeating decimal? First, note that a fraction in its lowest form with the denominator of 1502 will always have a repeating decimal if you divide the fraction (numerator divided by denominator).

Here we will count and show you the repeating digits when the numerator is 1 and denominator is 1502. In other words, we will show you the recurring digits you get when you calculate 1 divided by 1502.

Below is the answer to 1 divided by 1502 with the repeating decimals. We colored each interval of repeating decimals in different colors so it is easy for you to see. The repeating decimals (recurring digits) go on forever.

0.0006657789613848202396804260985352862849533954727030625832223701731025299600532623169107856191744340878828229027962716378162450066577896138482023968042609853528628495339547270306258322237017310252996005326231691078561917443408788282290279627163781624500665778961384820239680426098535286284953395472703062583222370173102529960053262316910785619174434087882822902796271637816245...

As you can see, the repeating digits are 00665778961384820239680426098535286284953395472703062583222370173102529960053262316910785619174434087882822902796271637816245 which will repeat indefinitely. When we counted the repeating decimals, we found that there are 125 repeating decimals in 1/1502 as a decimal.

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Denominator of 1503 as a repeating decimal
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Note that the answer above only applies to 1/1502. You will get a different answer if the numerator is different. Furthermore, 1502 as a denominator in a fraction is only repeating for sure if the fraction is in its lowest form possible.

Bonus: To communicate what numbers are repeating in a repeating decimal, you put a line (vinculum) over the repeating digits like this:

0.000665778961384820239680426098535286284953395472703062583222370173102529960053262316910785619174434087882822902796271637816245