What is the correct order, from least to greatest, of the numbers 0.0011, 0.0100, 0.0101, and 0.0110?
To determine the correct order of the given numbers -- 0.0011, 0.0100, 0.0101, and 0.0110 -- from least to greatest, you need to compare the digits from left to right.
Let's break down the numbers:
0.0011 can be read as decimal zero point zero zero one one
0.0100 can be read as decimal zero point zero one zero zero
0.0101 can be read as decimal zero point zero one zero one
0.0110 can be read as decimal zero point zero one one zero
Starting from the leftmost digit, we see that 0.0011, 0.0100, 0.0101, and 0.0110 all have a zero as the first digit after the decimal point. So, we need to compare the next digit.
Looking at the second digit after the decimal point, we have:
0.0011: 0
0.0100: 1
0.0101: 1
0.0110: 1
Since 0 is the lowest possible digit value and all other numbers have a 1 as the second digit, we can conclude that 0.0011 is the smallest number.
Next, we compare 0.0100, 0.0101, and 0.0110. As the second digit is same for all (1), we move to the third digit:
0.0100: 0
0.0101: 1
0.0110: 1
Comparing the third digit, we see that 0.0100 has a 0 in this position, while both 0.0101 and 0.0110 have 1s. Thus, 0.0100 is the smallest among the three.
Finally, comparing 0.0101 and 0.0110, we look at the fourth digit:
0.0101: 1
0.0110: 1
Since both numbers have the same digit in this position, we need to compare the fifth digit:
0.0101: 0
0.0110: 1
Since 0 is smaller than 1, we can conclude that 0.0101 is smaller than 0.0110.
Therefore, the correct order from least to greatest is:
0.0011, 0.0100, 0.0101, 0.0110.