Question

write the numbers in decreasing order.
-20, -0.51, -5√5, 4.93, 1/4
choose the correct answer below.
a. 1/4, 4.93, -20, -0.51, -5√5
b. -20, -5√5, -0.51, 1/4, 4.93
c. -5√5, -20, 4.93, 1/4, -0.51
d. 4.93, 1/4, -0.51, -5√5, -20

Explanation:

Step1: Calculate approximate value of \(-5\sqrt{5}\)

We know that \(\sqrt{5}\approx2.236\), so \(-5\sqrt{5}\approx - 5\times2.236=-11.18\)
And \(\frac{1}{4} = 0.25\)

Step2: Compare the numbers

Now we have the numbers: \(-20\), \(-0.51\), \(-11.18\) (approximate value of \(-5\sqrt{5}\)), \(4.93\), \(0.25\) (value of \(\frac{1}{4}\))

For positive numbers: \(4.93>0.25\)

For negative numbers, the larger the absolute value, the smaller the number.
\(\vert - 20\vert=20\), \(\vert - 11.18\vert = 11.18\), \(\vert-0.51\vert = 0.51\)
So \(-0.51>-11.18>-20\)

Combining positive and negative numbers, the decreasing order is: \(4.93,\frac{1}{4},- 0.51,-5\sqrt{5},-20\)

Answer:

D. \(4.93,\frac{1}{4}, - 0.51, - 5\sqrt{5}, - 20\)