Question

Without using a calculator, match each expression to the correct point.

f
de
←++ ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
-5
-3
Point Expression
3
2
d
e
-4
f
-√8
-π
-2
-1
+
0

Answer 1

d ↔ - π

e ↔ - √8

f ↔ - 3/2

Explanation:

Point d is to the left of -3

All points to the left of - 3 will be smaller than -3

Smaller than -3 means the absolute value will be greater than 3 but prefixed with a negative sign

Thus - 3.5 < - 3

-4 < -3

-99 < -3

etc

π = 3.14 approx

- π = - 3.14

- 3.14 < -3 and so it is to the left of -3. The only point to the left of -3 is point d

Similarly points to the right of -3 will have absolute values > 3 but prefixed by a negative sign

So -2.5, -2, -1, -0.5 etc are all greater than -3

√8 = √(4 · 2) = √4 · √2 = 2√2

√2 ≈ 1.414

so 2√2 ≈ 2.818

-√8 = - 2.818

so it is to the right of -3 but very close to -3

That would be point e

That leaves -3/2

-3/2 = - 1 1/2 and therefore lies halfway between -2 and - 1

That would be point f