Question

1. order the following sets of rational numbers from smallest to greatest (2 marks) - when you write your answers make sure you rewrite the letters on top of each number in order. honestly i am just marking the correct arrangement of the letters- answer in the boxes

a) \\(\

$$\begin{array}{cccccc} a & b & c & d & e & f \\\\ 1/4, & 0.5, & 3/5, & 2/3, & 0.081, & 0.79, \\end{array}$$

\\)

b) \\(\

$$\begin{array}{cccccc} a & b & c & d & e & f \\\\ -2/9, & -0.01, & -5/15, & -1, & -1/10, & -1.007 \\end{array}$$

\\)

Explanation:

Convert set a to decimals

To compare the numbers in set a, we convert each rational number to a decimal:

• \(A: \frac{1}{4} = 0.25\)
• \(B: 0.5\)
• \(C: \frac{3}{5} = 0.6\)
• \(D: \frac{2}{3} \approx 0.667\)
• \(E: 0.081\)
• \(F: 0.79\)

Order set a

Comparing the decimal values from smallest to greatest:

• \(0.081 < 0.25 < 0.5 < 0.6 < 0.667 < 0.79\)
• Corresponding letters: \(E < A < B < C < D < F\)

Convert set b to decimals

To compare the negative numbers in set b, we convert each to a decimal:

• \(A: -\frac{2}{9} \approx -0.222\)
• \(B: -0.01\)
• \(C: -\frac{5}{15} = -\frac{1}{3} \approx -0.333\)
• \(D: -1\)
• \(E: -\frac{1}{10} = -0.1\)
• \(F: -1.007\)

Order set b

For negative numbers, the larger the absolute value, the smaller the number:

• \(-1.007 < -1 < -0.333 < -0.222 < -0.1 < -0.01\)
• Corresponding letters: \(F < D < C < A < E < B\)

Answer:

Question a

Box 1	Box 2	Box 3	Box 4	Box 5	Box 6

Question b

Box 1	Box 2	Box 3	Box 4	Box 5	Box 6