Order the square root of 30, negative 5.5 repeating, 32 over 6, and negative five and two fifths from least to greatest.
a) negative five and two fifths, negative 5.5 repeating, the square root of 30, and 32 over 6
b) negative five and two fifths, negative 5.5 repeating, 32 over 6, and the square root of 30
c) negative 5.5 repeating, negative five and two fifths, 32 over 6, and the square root of 30
d) negative 5.5 repeating, the square root of 30, negative five and two fifths, and 32 over 6
The correct order from least to greatest is:
a) negative five and two fifths, negative 5.5 repeating, the square root of 30, and 32 over 6.
To order the given numbers from least to greatest, we need to compare their values. Let's compare each of them step by step:
1. Negative five and two fifths can be written as -5 2/5, which is equal to -27/5 as a fraction.
2. Negative 5.5 repeating can be represented as -5.5̅. Repeating decimals can be converted to fractions by using the concept of recurring decimals. Let x = -5.5̅, then multiplying x by 10 eliminates the repeating part. Hence, 10x = -55.5̅. Subtracting x = -5.5̅ gives 10x - x = -55.5̅ - (-5.5̅), which simplifies to 9x = -50. Now, dividing both sides by 9 gives x = -50/9.
3. The square root of 30 is a non-repeating decimal. Evaluating it gives approximately 5.477.
4. 32 over 6 can be simplified to 16 over 3 as both numerator and denominator can be divided by 2.
In comparing the numbers, we have:
-27/5 ≈ -5.4 (rounded to one decimal place)
-5.5̅ ≈ -6.1 (rounded to one decimal place)
√30 ≈ 5.5 (rounded to one decimal place)
16/3 = 5.333 (rounded to three decimal places)
From least to greatest, the order is:
c) negative 5.5 repeating, negative five and two fifths, 32 over 6, and the square root of 30.
To order these numbers from least to greatest, we need to compare them numerically. Let's evaluate each expression to get their approximate values:
a) The square root of 30 is approximately 5.477, negative 5.5 repeating is approximately -5.5, 32 over 6 is approximately 5.333, and negative five and two fifths is approximately -5.4.
b) Negative five and two fifths is approximately -5.4, negative 5.5 repeating is approximately -5.5, 32 over 6 is approximately 5.333, and the square root of 30 is approximately 5.477.
c) Negative 5.5 repeating is approximately -5.5, negative five and two fifths is approximately -5.4, 32 over 6 is approximately 5.333, and the square root of 30 is approximately 5.477.
d) Negative 5.5 repeating is approximately -5.5, the square root of 30 is approximately 5.477, negative five and two fifths is approximately -5.4, and 32 over 6 is approximately 5.333.
Comparing the approximate values, the correct order from least to greatest is:
b) negative five and two fifths, negative 5.5 repeating, 32 over 6, and the square root of 30