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Order the following numbers in ascending and descending order: a) 2.5, -12.4, -3.1 b) -9.5, -8.9, -10, -9.7 c) 3 1/2, -2 1/4, 1, -1 1/2 d) -1, -1.7, -12, 9.0

Mathematics

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13 steps

Part 1

Part a· 2 steps

2.5, -12.4, -3.1

  1. Arrange the numbers in ascending order (smallest to largest).

    −12.4,−3.1,2.5\boxed{\mathbf{-12.4, -3.1, 2.5}}

  2. Arrange the numbers in descending order (largest to smallest).

    2.5,−3.1,−12.4\boxed{\mathbf{2.5, -3.1, -12.4}}

Part b· 2 steps

9.5, -8.9, -10, -9.7

  1. Arrange the numbers in ascending order.

    −10,−9.7,−9.5,−8.9\boxed{\mathbf{-10, -9.7, -9.5, -8.9}}

  2. Arrange the numbers in descending order.

    −8.9,−9.5,−9.7,−10\boxed{\mathbf{-8.9, -9.5, -9.7, -10}}

Part c· 2 steps

3123\frac{1}{2}, −214-2\frac{1}{4}, 1, −112-1\frac{1}{2}

  1. Convert to decimal form for easier comparison

    3.5, −2.25-2.25, 1, −1.5-1.5. Arrange in ascending order.

    −214,−112,1,312\boxed{\mathbf{-2\frac{1}{4}, -1\frac{1}{2}, 1, 3\frac{1}{2}}}

  2. Arrange in descending order.

    312,1,−112,−214\boxed{\mathbf{3\frac{1}{2}, 1, -1\frac{1}{2}, -2\frac{1}{4}}}

Part d· 2 steps

1, -1.7, -12, 9.0

  1. Arrange the numbers in ascending order.

    −12,−1.7,−1,9.0\boxed{\mathbf{-12, -1.7, -1, 9.0}}

  2. Arrange the numbers in descending order.

    9.0,−1,−1.7,−12\boxed{\mathbf{9.0, -1, -1.7, -12}}

Part 2· 2 steps

The minimum overnight temperatures for one week at Mt. Wilhelm were 2∘C2^\circ C, 5∘C5^\circ C, 3∘C3^\circ C, 5∘C5^\circ C, 3∘C3^\circ C, 2∘C2^\circ C, 1∘C1^\circ C.

  1. Sum all the temperatures.

    Sum=2+5+3+5+3+2+1=21∘C\text{Sum} = 2 + 5 + 3 + 5 + 3 + 2 + 1 = 21^\circ C

  2. Divide the sum by the number of temperatures (7 days in a week).

    Average temperature=21∘C7=3∘C\text{Average temperature} = \frac{21^\circ C}{7} = \boxed{\mathbf{3^\circ C}}

Part 3· 3 steps

A lift is at the third basement floor (3 floors below ground level), and moves up 14 levels.

  1. Determine the starting level.

    "3 floors below ground level" can be represented as −3-3.

  2. Calculate the final level after moving up 14 levels.

    Final level=−3+14=11\text{Final level} = -3 + 14 = \boxed{\mathbf{11}}

    The lift ends up on the 11th floor.

  3. Represent this on a number line.

    Imagine a number line with 0 as ground level. Mark −3-3 as the starting point. Draw an arrow starting from −3-3 and extending 14 units to the right (upwards) to reach 11.

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