Question
Without actual division, show that the following rational numbers is a terminating decimal. Express in decimal form:$\frac{19}{3125}$
✓
Answer
$\frac{19}{3125}=\frac{19}{5^5}=\frac{19\times2^5}{5^5\times2^5}$$=\frac{608}{100000}=0.00608$
We know either 2 or 5 is not a factor of 19, so it is in its simplest form.
Moreover, it is in the form of $\left(2^m \times 5^n\right)$.
Hence, the given rational is terminating.
We know either 2 or 5 is not a factor of 19, so it is in its simplest form.
Moreover, it is in the form of $\left(2^m \times 5^n\right)$.
Hence, the given rational is terminating.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the mode of the following frequency distribution:
| Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
| Frequency | 8 | 7 | 12 | 5 | 3 |
What is the total number of factors of a prime number?
Two right circular cones have their heights in the ratio 1 : 3 and radii in the ratio 3 : 1, what is the ratio of their volumes?
Write the ratio in which the line segment doining the points A (3,-6) and B (5, 3) is divided by x-axis.
For what value of k, the roots of the equation $x^2+4 x+k=0$ are real?
→It P(2,p) is the mid-point of the line segment joining the points A (6, -5) and B (-2, 11), find the value of p.
In an $AP,$ if the common difference $(d)=-4,$ and the seventh term $\left(a_7\right)$ is $4 ,$ then find the first term.
→→
In a simultaneous throw of pair of dice, find the probability of getting:
A sum less than 7.
A sum less than 7.
Write the set of values of a and b for which the following system of equations has infinitely many solutions.
2x + 3y = 7
2ax + (a + b) y == 28
2x + 3y = 7
2ax + (a + b) y == 28