Order the numbers below from least to greatest.1/4 -4 sqrt(2) -3/2 4
-4
-3/2
1/4
4
sqrt(2)
To order the numbers from least to greatest, we need to arrange them in ascending order. Let's go step-by-step:
1/4, -4, √2, -3/2, 4
First, let's compare -4 and -3/2. We know that -4 is smaller than -3/2 since it is a negative number and has a larger absolute value. So, we have:
1/4, -4, √2, -3/2, 4 (Comparing -4 and -3/2: -4 < -3/2)
Next, let's compare √2 and -3/2. We can estimate that √2 is approximately 1.4, while -3/2 is approximately -1.5. Therefore, we have:
1/4, -4, √2, -3/2, 4 (Comparing √2 and -3/2: -3/2 < √2)
Now, we compare 1/4 and -3/2. To compare fractions, we can convert them to a common denominator. The LCD (least common denominator) for 4 and 2 is 4.
1/4 = 1/4 (since the denominator is already 4)
-3/2 = -6/4 (multiply the numerator and denominator by 2 to get a denominator of 4)
Now we can compare:
1/4, -4, √2, -3/2, 4 (Comparing 1/4 and -3/2: 1/4 < -3/2)
Finally, let's compare 1/4 and 4. It is clear that 1/4 is much smaller than 4.
1/4, -4, √2, -3/2, 4 (Comparing 1/4 and 4: 1/4 < 4)
Therefore, the numbers in ascending order from least to greatest are:
-4, -3/2, 1/4, √2, 4