Final answer:
To convert a repeating decimal to a fraction, follow a specific method that involves shifting the decimal point and performing calculations. In this case, the repeating decimal 0.370370370370... can be converted to the fraction -3330000/9999.
Step-by-step explanation:
A repeating decimal is a decimal that has a pattern of digits that repeats indefinitely. To convert a repeating decimal to a fraction, we can use the following method:
- Let x be the repeating decimal. Multiply both sides of the equation x = 0.
- Shift the decimal point of x to the right so that the repeating part is just to the right of the decimal point. Let y be the new number.
- Subtract y from x to get a new number z.
- Multiply z by a power of 10 equal to the number of digits in the repeating part of x.
- Subtract y from z to get a new number q.
- Divide q by a power of 10 equal to the number of digits in the repeating part of x, minus 1.
- Multiply q by 9 to get the numerator of the fraction.
- The denominator of the fraction is a number formed by as many nines as there are digits in the repeating part of x.
In this case, the repeating decimal 0.370370370370... can be converted to a fraction as follows:
x = 0.370370370370...
y = 1000x = 370.370370370...
z = x - y = 0.370370370... - 370.370370370... = -370
q = 1000z = -370000
Numerator of the fraction = 9q = -3330000
Denominator of the fraction = 9999 (4 nines because the repeating part has 3 digits)
Therefore, the fraction equivalent of the repeating decimal 0.370370370370... is -3330000/9999.
Learn more about Converting repeating decimals to fractions