0.37 Repeating as a Fraction in Simplest Form
In mathematics, a repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. One such example is 0.37, where the digits "37" repeat forever. But have you ever wondered what 0.37 repeating as a fraction in simplest form is?
Converting Repeating Decimals to Fractions
To convert a repeating decimal to a fraction, we can use the following steps:
- Let the repeating decimal be represented by x.
- Multiply both sides of the equation by 10^k, where k is the number of digits in the repeating pattern.
- Subtract the original equation from the new equation.
- Simplify the resulting equation to obtain the fraction.
Converting 0.37 Repeating to a Fraction
Let's apply the above steps to convert 0.37 repeating to a fraction:
- Let x = 0.373737...
- Multiply both sides by 100 (since the repeating pattern has 2 digits):
100x = 37.3737... 3. Subtract the original equation:
100x - x = 37.3737... - 0.3737... 99x = 37
- Divide both sides by 99:
x = 37/99
So, 0.37 repeating as a fraction in simplest form is 37/99.
Verification
To verify that 37/99 is indeed the correct fraction, we can convert it back to a decimal:
37 ÷ 99 = 0.373737...
As expected, the decimal expands to the original repeating decimal 0.37!
In conclusion, 0.37 repeating as a fraction in simplest form is 37/99.
