Show that $3.142678$ is a rational number. In other words,express $3.142678$ in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \ne 0$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) number is rational if it can be expressed in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \ne 0$.
Given the number $3.142678$,we can remove the decimal point by dividing by the appropriate power of $10$.
Since there are $6$ digits after the decimal point,we multiply and divide by $1,000,000$.
$3.142678 = \frac{3142678}{1000000}$.
This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor,which is $2$.
$\frac{3142678 \div 2}{1000000 \div 2} = \frac{1571339}{500000}$.
Since $1571339$ and $500000$ are integers and $500000 \ne 0$,the number $3.142678$ is a rational number.

Explore More

Similar Questions

Are the square roots of all positive integers irrational? If not,give an example of the square root of a number that is a rational number.

Simplify:
$(i)$ $2^{\frac{2}{3}} \cdot 2^{\frac{1}{3}}$
$(ii)$ $\left(3^{\frac{1}{5}}\right)^{4}$
$(iii)$ $\frac{7^{\frac{1}{5}}}{7^{\frac{1}{3}}}$
$(iv)$ $13^{\frac{1}{5}} \cdot 17^{\frac{1}{5}}$

State whether the following statements are true or false. Give reasons for your answers.
$(i)$ Every natural number is a whole number.
$(ii)$ Every integer is a whole number.
$(iii)$ Every rational number is a whole number.

Classify the following numbers as rational or irrational:
$(i)$ $\sqrt{23}$
$(ii)$ $\sqrt{225}$
$(iii)$ $0.3796$
$(iv)$ $7.478478 \ldots$
$(v)$ $1.101001000100001 \ldots$

Is zero a rational number? Can you write it in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \ne 0$?

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo