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What are the numbers shown by arrows (a) and (b) on the number line, and what is the midpoint between 0.5 and 2?

Mathematics

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Here are the solutions to the questions:

  1. The number shown by the arrow at (a) is...

  1. Observe the number line.

    The major markings are 0, 1, 2, 3. Between any two consecutive integers (e.g., 2 and 3), there are 9 smaller divisions, meaning each segment represents 0.1.

  2. Locate arrow (a).

    It is between 2 and 3. Counting down from 3, the first mark is 3−0.1=2.93 - 0.1 = 2.9. The second mark is 3−0.2=2.83 - 0.2 = 2.8.
    The number shown by arrow (a) is 2.8.
    The correct option is 2,8\boxed{\text{2,8}}.

    1. The number shown by the arrow at (b) is...

  3. Locate arrow (b).

    It is between 0 and 1. As established, each small division represents 0.1.

  4. Counting up from 0, the first mark is 0+0.1=0.10 + 0.1 = 0.1.

    The second is 0.2, the third is 0.3, and the fourth mark is 0+0.4=0.40 + 0.4 = 0.4.
    The number shown by arrow (b) is 0.4.
    The correct option is 0,4\boxed{\text{0,4}}.

    1. The number exactly halfway between 0,5 and 2 is ......

  5. To find the number exactly halfway between two numbers, calculate their average.

    The numbers are 0.5 and 2.

  6. Apply the midpoint formula

    $$
\text{Midpoint} = \frac{\text{Number 1} + \text{Number 2}}{2}
$$
$$
\text{Midpoint} = \frac{0.5 + 2}{2}
$$

  7. Perform the addition and division.

    $$
\text{Midpoint} = \frac{2.5}{2}
$$
$$
\text{Midpoint} = 1.25
$$
The number exactly halfway between 0.5 and 2 is 1.25.  
The correct option is $\boxed{\text{1,25}}$.
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