Without actual division, show that the following rational numbers… - Vidyadip

Question

Without actual division, show that the following rational numbers is a terminating decimal. Express in decimal form:
$\frac{17}{320}$

✓

Answer

$\frac{17}{320}=\frac{17}{2^6\times5}=\frac{17\times5^5}{2^6\times5^6}$
$=\frac{53125}{1000000}=0.053125$
We know either $2$ or $5$ is not a factor of $17$, 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.

Start Generating Free

Explore more

More "1 Marks Question" from Real Numbers→Real Numbers — all question types→Maths STD 10 question papers→Gujarat Board STD 10 question papers→Gujarat Board question paper generator→

Similar questions

For any data Median $=120$, Mean $=119$ then find

For the AP: $\frac { 3 } { 2 } , \frac { 1 } { 2 } , -\frac {1 } { 2 } , -\frac {3} {2}$, ... write the first term a and the common difference d.

A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability?
That the sum of the two numbers that turn up is $7?$

Find the roots of the quadratic equation $2x^2-x+{1 \over8} = 0$ by factorization.

Solve the equations: $2 x+y=6$ and $4 x+2 y=5$.

Check the equation is quadratic equation or not:$(x - 3) (2x + 1) = x(x + 5)$

If tangents $PA$ and $PB$ from a point $P$ to a circle with centre $O$ are inclined to each other at angle of $80^\circ$, $\angle$$POA$ is equal to

The string of a kite is $100m$ long and it makes an angle of $60^\circ$ with the horizontal. If these is no slack in the string, the height of the kite from the ground is:

What is the smallest prime number ?

Prove the given identity, where the angles involved are acute angles for which the expressions are defined. $( cosec\; \theta - \cot \theta ) ^ { 2 } = \frac { 1 - \cos \theta } { 1 + \cos \theta }$