Which is the decimal expansion of 7/22

The decimal expansion of 7/22 is 0.3181818181…, which is a repeating decimal.
This means it continues indefinitely with the “18” repeating. You can represent this as 0.31̅81̅, where the bar over “18” indicates the repeating part.
To find this decimal, divide 7 by 22. You will see that 7 doesn’t go into 22, so you add a decimal point and zeros.
When you perform the division, you get 0.318181…, showing that it cycles through “18” repeatedly.
Understanding repeating decimals can be very useful in math, especially when dealing with fractions.
Some might wonder how to convert a repeating decimal back into a fraction.
It’s quite simple: let x equal the repeating decimal, multiply by a power of ten to move the decimal point, and then subtract to isolate x.
This process confirms that 7/22 equals 0.318181…, which is a common fraction-to-decimal conversion.

How do you convert 0.318181… back to a fraction?

To convert 0.318181… to a fraction, let x = 0.318181… . Multiply by 100 to get 100x = 31.8181… . Subtract the original x from this equation to isolate x and solve for the fraction, resulting in 7/22.

What is a repeating decimal?

A repeating decimal is a decimal fraction that eventually repeats a sequence of digits indefinitely. For example, 0.333… or 0.666… are repeating decimals.

Is 7/22 a rational number?

Yes, 7/22 is a rational number because it can be expressed as a fraction of two integers, with a non-zero denominator.

Why is it important to understand repeating decimals?

Understanding repeating decimals helps in converting between fractions and decimals, performing calculations, and grasping concepts of limits and sequences in mathematics.

What other fractions have repeating decimals?

Many fractions have repeating decimals, such as 1/3 (0.333…) and 1/6 (0.1666…). Any fraction where the denominator has prime factors other than 2 or 5 will often result in a repeating decimal.

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