Order the numbers from least to greatest: 1/2, √12, 0.666666666....., -1/10, 6.33333....
-1/10, 1/2, 0.666666666....., √12, 6.33333....
To order the numbers from least to greatest, let's begin by simplifying the given numbers:
1/2 is a fraction, and since it is less than 1, it is smaller than all the other numbers.
√12 can be simplified as √(4 * 3), which further simplifies to 2√3.
0.666666666..... is a repeating decimal, which can be written as 2/3.
-1/10 is a negative fraction, and it is smaller than all the other numbers so far.
6.33333.... is a repeating decimal, which can be written as 19/3.
Now, let's arrange the numbers in ascending order:
-1/10, 1/2, 2√3, 2/3, 19/3
So, the numbers in ascending order are: -1/10, 1/2, 2√3, 2/3, 19/3.
To order the numbers from least to greatest, you need to compare their values. Let's go through each of the numbers step by step:
1/2: This fraction represents a value between 0 and 1, and it is smaller than 1.
√12: To compare this with other numbers, we need to approximate its value. Without a calculator, we can use estimation. The square root of 12 is between √9 (which is 3) and √16 (which is 4). So, √12 is a little bigger than 3.
0.666666666...: This is a recurring decimal, meaning that the number 6 repeats indefinitely. We can approximate this by looking at the pattern, which repeats after 6. So, we can write it as 0.6.
-1/10: This fraction represents a negative value between 0 and -1. Our other numbers are all positive, so this will be the smallest.
6.33333...: This is another recurring decimal, and if we look at the repeating pattern, it is clearly greater than 6. We can approximate it by rounding to one decimal place, making it 6.3.
Now, let's order the numbers from least to greatest:
-1/10 < 1/2 < √12 < 0.6 < 6.3
So, the numbers in order from least to greatest are: -1/10, 1/2, √12, 0.6, 6.3.