If 1.525252.... is converted to a fraction, then what is the sum of its numerator and denominator?
Given :
Given decimal number is 1.525252....
To find :
We have to convert it into a fraction.
Solution :
Let x = 1.525252...
Multiply it by 100 on both sides.
This implies,
100x = $100\times1.525252.....$
100x = 152.525252....
Subtract x from 100x to get,
$100x-x=152.525252.....-1.525252.....$
99x = 151
x=$\frac{151}{99}$
The required fraction is $\frac{151}{99}$.
Therefore, the sum of the numerator and denominator = $151+99=250.$
Related Articles
- The numerator of a fraction is 4 less than the denominator. If the numerator is decreased by 2 and denominator is increased by 1, then the denominator is eight times the numerator. Find the fraction.
- The numerator of a fraction is 3 less than the denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is $\frac{29}{20}$. Find the original fraction.
- The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.
- The denominator of a fraction is 4 more than twice its numerator. Denominator becomes 12 times the numerator. If both the numerator and the denominator are reduced by 6. Find the fraction.
- The sum of numerator and denominator of a fraction is 3 less than twice the denominator. If each of the numerator and denominator is decreased by 1, the fraction becomes $\displaystyle \frac{1}{2}$, find the fraction.
- The sum of a numerator and denominator of a fraction is 18. If the denominator is increased by 2, the fraction reduces to $\frac{1}{3}$. Find the fraction.
- The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes $\frac{1}{2}$. Find the fraction.
- A fraction becomes $\frac{1}{3}$ if 1 is subtracted from both its numerator and denominator. If 1 is added to both the numerator and denominator, it becomes $\frac{1}{2}$. Find the fraction.
- The sum of the numerator and denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator are increased by 3, they are in the ratio $2 : 3$. Determine the fraction
- The numerator of a fraction is 6 less than the denominator. If 3 is added to the numerator, the fraction is equal to $\frac{2}{3}$. What is the original fraction equal to?
- If the numerator of a fraction is multiplied by 2 and the denominator is reduced by 5 the fraction becomes $\frac{6}{5}$. And, if the denominator is doubled and the numerator is increased by 8, the fraction becomes $\frac{2}{5}$. Find the fraction.
- In a fraction, twice the numerator is 2 more than the denominator. If 3 is added to the numerator and denominator the new fraction is $\frac{2}{3}$. Find the original fractions.
- The denominator of a fraction is 7 more than its numerator. If '1' is subtracted from both the numerator and the denominator, it becomes $\frac{9}{6}$. Form an equation to find the value of the actual fraction.
- A fraction becomes $\frac{9}{11}$ if 2 is added to both numerator and the denominator. If 3 is added to both the numerator and the denominator, it becomes $\frac{5}{6}$. Find the fraction.
- What is the Numerator and the Denominator?
Kickstart Your Career
Get certified by completing the course
Get Started