0.142857 repeating as a fraction

How it gets there

1. Call the number x, so x = 0.(142857). It cannot go over a power of ten the way a terminating decimal can, because the digits never stop.
2. Multiply by 1,000,000, so that it and the original have the same endless tail: 1,000,000x = 142857.142857… against x = 0.142857…
3. Subtract. The tails are identical, so everything after the point cancels exactly: 999,999x = 142,857, which is 142857/999999.
4. Divide both by 142857: 1/7.

Questions people actually ask

What is half of 0.(142857)?

1/14 — a repeating decimal, so the fraction is the only exact way to write it. Halving a fraction doubles the denominator rather than halving the top, unless the numerator is even and cancels. Doubled instead, 1/7 is 2/7.

What is 0.(142857) as a fraction?

1/7, in lowest terms. 142857/999999 is the same value before reducing, and dividing both by 142857 gets there.

Why can't 0.(142857) be written over a power of ten?

Because the digits never stop, and a power of ten only clears a decimal that terminates. The algebra above multiplies by two different powers of ten so the endless tails line up, then subtracts them away — which is the standard proof that every repeating decimal is a rational number.

Is 0.(142857) a rational number?

Yes. A number is rational exactly when it can be written as one whole number over another, and 1/7 is that. Every repeating decimal is rational and every rational number's decimal either terminates or repeats — the two statements are the same fact from opposite ends.

Is 1/7 in simplest form?

Yes. The numerator and denominator share no factor above 1, which is what simplest form means. 142857/999999 is the same number written before that reduction.

What is 0.(142857) on a tape measure?

It falls between marks. The nearest sixteenth is 1/8, which is off by about 0.45 mm on an inch — close enough for carpentry and not for machining.

What is 1/7 as a decimal?

0.(142857). This page runs the conversion in the direction people ask for it, and dividing 1 by 7 runs it back the other way.

The same number, other ways

Fraction, lowest terms

1/7

Before reducing

142857/999999

As a percentage

14.285…%

As a ratio

1:7

Equivalent fractions

2/14, 3/21, 4/28, 5/35

Nearest sixteenth on a tape

1/8 (nearest)

A tape measure only has sixteenths, so 0.(142857) does not land on a mark. The nearest one is 1/8, which is 0.286 of a sixteenth away — about 0.45 mm on an inch.

Work it out for any decimal

The two calculators this page is built from take any numbers you like: reduce a fraction shows the divisor it used, and fraction to decimal goes the other way, to the nearest 16th, 32nd and 64th.

Decimals either side

Cite this page

APA

Rule Calculator. (2026). 0.142857 repeating as a fraction. Rule Calculator. https://rulecalculators.com/fraction/0-142857-repeating-as-a-fraction

MLA

"0.142857 repeating as a fraction." Rule Calculator, October 1, 2026, https://rulecalculators.com/fraction/0-142857-repeating-as-a-fraction.

Chicago

Rule Calculator. "0.142857 repeating as a fraction." Rule Calculator. Last reviewed October 1, 2026. https://rulecalculators.com/fraction/0-142857-repeating-as-a-fraction.

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