Question
Without actually performing the long division, state whether state whether the following rational numbers will have a terminating decimal expansion or a non terminating repeating decimal expansion.
$\frac{77}{210}$
$\frac{77}{210}$
✓
Answer
The given number is $\frac{77}{210}$ and HCF$(77, 210) = 7.$
$\therefore\ \frac{77}{210}=\frac{77\div7}{210\div7}=\frac{11}{30}$
Here, $\frac{11}{30}$ is in its simplest form.
Here, $\frac{77}{210}$ is in its simplest form.
Now, $30 = 2 \times 3 \times 5$ is not of the form $2^m \times 5^n.$
So, the given number has a non-terminating repeating decimal expansion.
$\therefore\ \frac{77}{210}=\frac{77\div7}{210\div7}=\frac{11}{30}$
Here, $\frac{11}{30}$ is in its simplest form.
Here, $\frac{77}{210}$ is in its simplest form.
Now, $30 = 2 \times 3 \times 5$ is not of the form $2^m \times 5^n.$
So, the given number has a non-terminating repeating decimal expansion.
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
In ΔPQR seg PM is a median. Angle bisectors of ∠PMQ and ∠PMR intersect side PQ and side PR in points X and Y respectively. Prove that XY || QR.
Complete the proof by filling in the boxes. In $\triangle PMQ$, ray MX is bisector of $\angle PMQ$.
$\therefore\frac{\square}{\square}=\frac{\square}{\square}......... (I)$ theorem of angle bisector.
In $\triangle PMR$, ray MY is bisector of $\angle PMR$.
$\therefore\frac{\square}{\square}=\frac{\square}{\square}.........(II)$ theorem of angle bisector.
But $\frac{M P}{M Q}=\frac{M P}{M R}$ $\qquad$
$\therefore \frac{ PX }{ XQ }=\frac{ PY }{ YR }$ $\qquad$
$\therefore XY||QR......$ converse of basic proportionality theorem.
→Complete the proof by filling in the boxes. In $\triangle PMQ$, ray MX is bisector of $\angle PMQ$.
$\therefore\frac{\square}{\square}=\frac{\square}{\square}......... (I)$ theorem of angle bisector.
In $\triangle PMR$, ray MY is bisector of $\angle PMR$.
$\therefore\frac{\square}{\square}=\frac{\square}{\square}.........(II)$ theorem of angle bisector.
But $\frac{M P}{M Q}=\frac{M P}{M R}$ $\qquad$
$\therefore \frac{ PX }{ XQ }=\frac{ PY }{ YR }$ $\qquad$
$\therefore XY||QR......$ converse of basic proportionality theorem.
In $\triangle A B C, A P$ is a median. If $A P=7, A B^2+A C^2$ $=260$, find $B C$.
→Evaluate:
$ \frac{\cos58^\circ}{\sin32^\circ}+\frac{\sin22^\circ}{\cos68^\circ}-\frac{\cos38^\circ\text{cosec }52^\circ}{\tan18^\circ\tan35^\circ\tan60^\circ\tan72^\circ\tan65^\circ}$
→$ \frac{\cos58^\circ}{\sin32^\circ}+\frac{\sin22^\circ}{\cos68^\circ}-\frac{\cos38^\circ\text{cosec }52^\circ}{\tan18^\circ\tan35^\circ\tan60^\circ\tan72^\circ\tan65^\circ}$
A trader from Surat, Gujarat sold cotton clothes to a trader in Rajkot, Gujarat. The taxable value of cotton clothes is Rs. 2.5 lacs. What is the amount of GST at 5% paid by the trader in Rajkot?
A(15,5), B(9,20) and A-P-B. Find the ratio in which point P(11,15) divides segment AB.
A card is drawn at random from a pack of well shuffled 52 playing cards. Find the probability that the card drawn is -
an ace.
an ace.
If $\sec \theta=\frac{25}{7}$, find the value of $\tan \theta$.
→Solve the following quadratic equation by factorization.
$7 m^2=21 m$
→$7 m^2=21 m$
Draw an ogive to represent the following frequency distribution:
|
Class-interval
|
0-4
|
5-9
|
10-14
|
15-19
|
20-24
|
|
No. of students
|
2
|
6
|
10
|
5
|
3
|