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Express the repeating decimal 0.37373737373737… as a fraction

User Hypehuman
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Final answer:

The repeating decimal 0.373737... can be expressed as the fraction 37/99. The process involves multiplication by 100 to separate out the repeating part, and then subtraction to solve for x.

Step-by-step explanation:

To express the repeating decimal 0.37373737373737... as a fraction, we can use the method for converting repeating decimals to fractions. Let's represent the decimal as x:

x = 0.373737...

To separate out the repeating decimal part, we can multiply x by 100 (since the repeating part is in the 100ths and 1000ths places), which gives:

100x = 37.373737...

Then, subtract the original equation (x) from this result:

100x - x = 37.373737... - 0.373737...

So, 99x = 37

Solving for x, we get:

x = 37 / 99

So, the repeating decimal 0.373737... can be expressed as the fraction 37/99.

Learn more about Repeating Decimal

User U And Me
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