Order the following numbers from least to greatest. sqrt(11), - 0.4, (- 4/3) 0.8, sqrt(2)
Ordering the numbers from least to greatest:
(-4/3) 0.8, -0.4, sqrt(2), sqrt(11)
To order the numbers from least to greatest, let's compare them step-by-step.
1. The given numbers are:
sqrt(11), -0.4, (-4/3), 0.8, sqrt(2)
2. Let's compare sqrt(11) and -0.4:
-0.4 < sqrt(11)
3. Next, let's compare -0.4 and (-4/3):
-4/3 < -0.4
4. Now, let's compare (-4/3) and 0.8:
-4/3 < 0.8
5. Finally, let's compare 0.8 and sqrt(2):
sqrt(2) < 0.8
Thus, the numbers in order from least to greatest are:
-4/3, -0.4, sqrt(11), sqrt(2), 0.8
To order the numbers from least to greatest, we need to compare their values. Here's how you can do it step by step:
1. Start with the given numbers: sqrt(11), -0.4, (-4/3) 0.8, and sqrt(2).
2. First, let's compare the two square roots, sqrt(11) and sqrt(2). Since both numbers are positive, we can compare them directly. However, comparing square roots can be a bit tricky mentally, so let's use a calculator to find their decimal approximations:
- sqrt(11) ≈ 3.3166...
- sqrt(2) ≈ 1.4142...
So, sqrt(2) is smaller than sqrt(11) because 1.4142... is smaller than 3.3166....
3. Next, compare -0.4 with the largest of the two square roots we just compared, sqrt(11). Since -0.4 is negative and sqrt(11) is positive, we know that -0.4 is smaller than sqrt(11).
4. Now let's compare the remaining two fractions, (-4/3) 0.8 and sqrt(2). Even though (-4/3) 0.8 might look complex, it's actually a single number. Let's simplify it: -4/3 ≈ -1.3333..., so (-4/3) 0.8 ≈ -1.3333... × 0.8 ≈ -1.0666....
Comparing this with sqrt(2) (≈ 1.4142...), we can see that (-4/3) 0.8 is smaller since -1.0666... is less than 1.4142....
5. Finally, we have -0.4 < (-4/3) 0.8 < sqrt(2) < sqrt(11).
So, from least to greatest, the order is: -0.4, (-4/3) 0.8, sqrt(2), sqrt(11).
Remember, decimal approximations were used for comparison purposes only.