0.037 Repeating as a Fraction in Simplest Form
What is 0.037 Repeating?
0.037 repeating is a decimal number that has a pattern of 037 repeating indefinitely. It can be written as 0.037037037... where the sequence "037" goes on forever.
Converting 0.037 Repeating to a Fraction
To convert 0.037 repeating to a fraction, we can use the following steps:
Let x = 0.037037037...
Multiply both sides by 1000, since there are three digits in the repeating sequence:
1000x = 37.037037...
Subtract x from both sides to eliminate the repeating decimal:
999x = 37
Divide both sides by 999:
x = 37/999
So, 0.037 repeating as a fraction in simplest form is:
37/999
Verification
To verify that 37/999 is the correct fraction, we can divide the numerator by the denominator:
37 ÷ 999 = 0.037037037...
Which is indeed the original repeating decimal.
Conclusion
In conclusion, 0.037 repeating as a fraction in simplest form is 37/999. This conversion can be useful in various mathematical calculations and applications where fractions are preferred over decimals.
