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Plot -2.8 on the numberline. What number does the arrow point to on the number line? Write the next three multiples of 17.

Mathematics

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Here are the solutions to the problems:

1. Plot -2.8 on the numberline.

  1. Locate -2 on the number line.

  2. Move 8 small divisions to the left from -2.

    Each small division represents 0.1.
    The point for -2.8 is between -3 and -2, specifically 8 divisions to the left of -2.

    Working out:

    −2−0.8=−2.8-2 - 0.8 = -2.8

    Answer:
    The point is marked on the number line below.

    ←——−4——−3——∙—−2——−1——0——1——2——3→\leftarrow\text{---}\underset{-4}{\text{---}}\text{---}\underset{-3}{\text{---}}\text{---}\underset{\color{red}{\bullet}}{\text{---}}\underset{-2}{\text{---}}\text{---}\underset{-1}{\text{---}}\text{---}\underset{0}{\text{---}}\text{---}\underset{1}{\text{---}}\text{---}\underset{2}{\text{---}}\text{---}\underset{3}{\text{---}}\rightarrow

    The red dot indicates the position of -2.8.

    2. What number does the arrow point to on the number line?

  3. Identify the integers surrounding the arrow.

    The arrow is between -2 and -1.

  4. Count the number of small divisions from -2 towards -1.

    There are 10 small divisions between each integer, so each division represents 0.1.

  5. The arrow points to the second division to the right of -2.

    Working out:

    −2+(2×0.1)=−2+0.2=−1.8-2 + (2 \times 0.1) = -2 + 0.2 = -1.8

    Answer:
    The arrow points to −1.8\boxed{\mathbf{-1.8}}.

    3. Write the next three multiples of 17.
    17, 34, 51, 68, 85, ____, ____, ____

  6. Identify the pattern.

    The numbers are multiples of 17.
    The given numbers are 17×117 \times 1, 17×217 \times 2, 17×317 \times 3, 17×417 \times 4, 17×517 \times 5.

  7. Calculate the next three multiples (17×617 \times 6, 17×717 \times 7, 17×817 \times 8).

    Working out:

    17×6=10217 \times 6 = 102 17×7=11917 \times 7 = 119 17×8=13617 \times 8 = 136

    Answer:
    The next three multiples are 102,119,136\boxed{\mathbf{102, 119, 136}}.

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