The completed sentence is as follows:
- Every point on the number line corresponds to a real number which many be either rational or irrational.
- The decimal form of an irrational number is neither terminating nor repeating.
- The decimal representation of a rational number is either terminating or non-terminating recurring.
- Every real number is either rational number or an irrational number.
What is the representation of the √3.5, √9.4, √10.5 on the real number line?
For √3.5:
- Draw the first section of the line AB = 3.5 units.
- Produce B up until point C in step 2 such that BC equals one unit.
- Step 3: Locate AC's midpoint, let's say O.
- Step 4: Draw a semicircle across A and C, using O as the center.
- Step 5: Sketch a line through B that is parallel to OB and cuts a semicircle at D.
- Step 6: Draw an arc cutting the OC formed at E using B as the center and BD as the radius.
It is to be noted that in the right angled triangle named OBD:
In right ΔOBD,
BD² = OD² – OB²
= OC² – (OC – BC)² this is because OD = OC
BD² = 2OC x BC – (BC)²
= 2 x 2.25 x 1 – 1
= 3.5 => BD
= √3.5
For √9.4
Enumerate a line segment labelled AB = 9.4 units; then
Repeat the same steps that were given above.
BD² = 2OC x BC – (BC)²
= 2 x 5.2 x 1 – 1
= 9.4
=> BD = √9.4
For √10.5
Enumerate a line segment AB = 10.5 units.
Repeat steps 2-6 above;
B²2 = 2OC x BC – (BC)²
= 2 x 5.75 x 1 – 1
= 10.5
=> BD = √10.5
Learn more about irrational number at;
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