Find an equivalent fraction for the decimal number. In your final answer, include all of your work.

0.901 recurring

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Find an equivalent fraction for the decimal number. In your final answer, include all of your work.

0.901 recurring

Answer :

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calculista calculista · Answer 1 · 2025-03-22T02:57:33-04:00

Answer:

[tex]\frac{901}{999}[/tex]

Step-by-step explanation:

we know that

A Recurring Decimal, is a decimal number with a digit (or group of digits) that repeats forever.

In this problem we have

0.901 recurring

that means

0.901901901..

Let

[tex]x=0.901901901..[/tex]

Multiply x by a power of [tex]10[/tex], one that keeps the decimal part of the number the same:

[tex]1,000x=901.901901..[/tex]

Subtract [tex]x[/tex] from [tex]\\1000x[/tex]

[tex]1,000x-x=901.901901..-0.901901..=901[/tex]

The repeating decimals should cancel out

[tex]\\999x=901[/tex]

solve for x

Divide by [tex]999[/tex] both sides

[tex]990x/990=135/990[/tex]

[tex]x=\frac{901}{999}[/tex]

Find an equivalent fraction for the decimal number. In your final answer, include all of your work. 0.901 recurring

Answer :

Other Questions

Find an equivalent fraction for the decimal number. In your final answer, include all of your work.

0.901 recurring