represent each of the following numbers on the real line root 3 please solve step by step please its urgent
Answers
Answer:
Draw a line and locate the point having the coordinate as ‘0’. This point is known as the origin.
Rational numbers
If the given number is positive, locate it on the right side of the origin. If it is a negative number, locate it on the left side of zero.
Divide each unit into the values which are equal to the denominator of the fraction. For example: for representing 4/5 on the number line you need to divide each unit into 5 subunits.
Example: Represent 2/3 on a number line.
Solution: 2/3 is a positive rational number and it is known that 2/3 is less than 1 and greater than 0. Therefore, 2/3 lies between 0 and 1 on the number line.
Here, the denominator is 3 so we will divide each unit length into 3 subunits between 0 and 1.
Rational numbers
We know every rational number can be expressed as decimal expansions. Here,
⅔= 0.6666666666666667.....✨✌
Step-by-step explanation:
First draw a number line having points (at least) [0,3]. If we denote the point 0 as “O” and point 1 as “A” then OA will be equal to 1 unit. Then at point A draw a perpendicular of length AB=1 unit ( equal to the distance from 0 to 1 in the number line i.e. OA). And join the points O and A, so that OAB is a right angled triangle. Then by pythagoras theorem,
OB^2=OA^2+AB^2
=> OB=sqrt (1^2+1^2)
=>OB = root2
Now, again draw a perpendicular at point B of length BC= 1 unit and join the points O and C. Again by pythagoras theorem we get OC = root 3. Then by compus taking radius =OC, draw an arc so that it cuts the number line at D. Then the distance OD will be the square root of 3.
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