Question

Which of the following shows the correct order for -1 2/5, (-1)², -1.4 repeating and (1/2)²



a.
(-1)²<-1.4 repeating< -1 2/5<(1/2)²

b.
-1.4 repeating<-1 2/5<(1/2)²<(-1)²

c.
-1 2/5<-1.4 repeating<(1/2)²<(-1)²
​

Answer 1

Answer:

b. -1.4 repeating<-1 2/5<(1/2)²<(-1)²

Step-by-step explanation:

Calculate and convert the fractions (mixed number) to the decimals:

$-1\dfrac{2}{5}=-1\dfrac{2\cdot2}{5\cdot2}=-1\dfrac{4}{10}=-1.4\\\\(-1)^2=(-1)(-1)=1\\\\-1.4444...\\\left(-\dfrac{1}{2}\right)^2=\left(-\dfrac{1}{2}\right)\left(-\dfrac{1}{2}\right)=\dfrac{1}{4}=\dfrac{1\cdot25}{4\cdot25}=\dfrac{25}{100}=0.25$

We have

$-1.4;\ 1,\ -1.444...,\ 0.25$

Therefore

$-1.444...<-1.4<0.25<1\\.\qquad\qquad\Downarrow\\-1.\overline{4}<-1\dfrac{2}{5}<\left(\dfrac{1}{2}\right)^2<(-1)^2$