What is the order of the following numbers from least to greatest?
32) sqrt(3) - 2.5, - 5/4 , a. - 2.5, b. 2.5, - 2/3 - 5/4 5/(4 ^ o) - 2/3 -를, |- 4| 0.75, sqrt(3), 1.9, |- 4| 0.75, sqrt(3) 1.9, |- 4|
c. 2.5, - 2/3 - 5/(4') sqrt(3) 0.75, 1.9, |- 4|
d. - 2.5, - 5/4 - 2/3 sqrt(3) 0.75, 1.9, |- 4|
The order of the numbers from least to greatest is:
c. 2.5, - 2/3, - 5/4, sqrt(3), 0.75, 1.9, |-4|
To find the order of the given numbers from least to greatest, let's simplify and arrange them individually:
1. sqrt(3) - 2.5
2. -5/4
3. -2.5
4. 2/3 - 5/4
5. 5/(4^o) - 2/3
6. -|-4|
7. 0.75
8. sqrt(3)
9. 1.9
10. |-4|
Now let's arrange them in ascending order:
-|-4|, -5/4, -2.5, 2/3 - 5/4, 5/(4^o) - 2/3, 0.75, sqrt(3) - 2.5, 1.9, sqrt(3), |-4|
Therefore, the correct order from least to greatest is:
c. -|-4|, -5/4, -2.5, 2/3 - 5/4, 5/(4^o) - 2/3, 0.75, sqrt(3) - 2.5, 1.9, sqrt(3), |-4|
To order the given numbers from least to greatest, follow these steps:
Step 1: Simplify each number and rewrite them in a standard form that is easier to compare.
The given numbers are:
32) sqrt(3) - 2.5,
- 5/4,
- 2.5,
2/3,
- 5/4,
5/(4 ^ o),
- 2/3,
- 4,
0.75,
sqrt(3),
1.9,
- 4,
0.75,
sqrt(3),
1.9,
- 4
Converting each number to decimal form:
32) sqrt(3) - 2.5 ≈ 0.732 - 2.5 ≈ -1.768,
- 5/4 ≈ -1.25,
- 2.5 as it is,
2/3 ≈ 0.667,
- 5/4 ≈ -1.25,
5/(4 ^ o) = 5/1 = 5,
- 2/3 ≈ -0.667,
- 4 as it is,
0.75 as it is,
sqrt(3) ≈ 1.732,
1.9 as it is,
- 4 as it is,
0.75 as it is,
sqrt(3) ≈ 1.732,
1.9 as it is,
- 4 as it is.
The numbers in decimal form are:
-1.768, -1.25, -2.5, 0.667, -1.25, 5, -0.667, -4, 0.75, 1.732, 1.9, -4, 0.75, 1.732, 1.9, -4.
Step 2: Arrange the numbers in ascending order.
-2.5, -1.768, -1.25, -1.25, -0.667, -0.667, 0.667, 0.75, 0.75, 1.732, 1.732, 1.9, 1.9, 5, -4, -4, -4.
Step 3: Rewrite the numbers in simplified form.
-2.5, -1.768, -1.25, -1.25, -0.667, -0.667, 0.667, 0.75, 0.75, 1.732, 1.732, 1.9, 1.9, 5, -4, -4, -4.
Therefore, the correct order of the given numbers from least to greatest is:
c. -2.5, -1.768, -1.25, -1.25, -0.667, -0.667, 0.667, 0.75, 0.75, 1.732, 1.732, 1.9, 1.9, 5, -4, -4, -4.