To do:We have to find the maximum number of digits in the repeating block of digits in the decimal expansion of \( \frac{1}{17} \).Solution:Dividing 1 by 17 using the long division method, we get, 17)100(0.0588235294117647      85---------      150      136  ---------       140      ... Read More

To do:We have to write three numbers whose decimal expansions are non-terminating non-recurring.Solution:A rational number can be expressed in either terminating decimal or non-terminating recurring decimals and an irrational number is expressed in non-terminating non-recurring decimals.Therefore, $\sqrt7=2.64575131106......$, $\sqrt{23}=4.7958315......$ and $\sqrt{31}=5.567764363........$ are three numbers whose decimal expansions are non-terminating non-recurring.Read More

Given:Given number is $3.765$.To do:We have to visualise the representation of $3.765$ on the number line using successive magnification.Solution:$3.765$ lies between 3 and 4.So, we divide the number line into 10 equal parts and mark each point of division. The first mark on the right of 3 will be $3.1$ ... Read More

To do:We have to draw an angle of $40^o$ and its supplementary angle.Solution:Steps of construction:(i) Let us draw a line $l$ and mark points $P$, $O$ and $Q$ on it. Now, let us place the centre of the protractor on the point $O$ and mark a point $A$ at an ... Read More

To do:We have to draw an angle of $70^o$ and make a copy of it using only a straight edge and compasses.Solution:Steps of construction:(i) Let us draw a line $l$ and mark a point $O$ on it. Now, let us mark a point $A$ at a measure of $70^o$ by ... Read More

To do: We have to draw an angle of measure $135^o$ and bisect it.Solution:Steps of construction:(i) Let us draw a line $l$ and mark a point $O$ on it.(ii) Now, by placing a protractor on the point $O$ let us mark a point $P$ at a measure of $135^o$.(iii) Now, by ... Read More

To do:We have to draw an angle of measure $45^o$ and bisect it.Solution:Steps of construction:(i) Let us draw a line $l$ and mark a point $O$ on it.(ii) Now, by placing a protractor on the point $O$ let us mark a point $P$ at a measure of $45^o$.(iii) Now, by ... Read More

To do:We have to construct angles of given measures.Solution:(a) Steps of construction:(i) Let us draw a line $l$ of any length and mark a point $P$ on the line $l$.(ii) Now, by taking compasses with any radius let us draw an arc from point $P$ and mark the point of intersection ... Read More

To do:We have to draw an angle of measure $153^o$ and divide it into four equal parts.Solution:Steps of construction:(i) Let us draw a line $l$ of any length and mark a point $P$ on it.(ii) Now, by taking a protractor let us place the centre of the protractor on the ... Read More

To do:We have to draw a right angle and construct its bisectors.Solution:Steps of construction:(i) Let us draw a line of any length $l$ and mark a point $O$ on it.(ii) By taking compasses with any measure of radius let us draw an arc from point $O$ and mark the point ... Read More