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If the radius is sqrt(3) m, write down two other irrational numbers the learners may encounter in similar measurements.

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4. If the radius is 3\sqrt{3} m, write down two other irrational numbers the learners may encounter in similar measurements.

An irrational number is a number that cannot be expressed as a simple fraction and has a non-repeating, non-terminating decimal expansion.
Two other irrational numbers could be:

  • 2\sqrt{2} m
  • π\pi m

5. A shopkeeper buys sugar totalling 4124 \frac{1}{2} kg. Express this in improper fraction.

  1. Convert the mixed number to an improper fraction.

    412=(4×2)+124 \frac{1}{2} = \frac{(4 \times 2) + 1}{2}

  2. Calculate the numerator.

    =8+12= \frac{8 + 1}{2}

  3. Simplify the fraction.

    =92 kg= \boxed{\frac{9}{2} \text{ kg}}

    6. A teacher asks learners to find the reciprocal of the number of hours they spend online each day. If a learner spends 34\frac{3}{4} hours online daily, find the reciprocal.

  4. Identify the number of hours spent online.

    Hours=34\text{Hours} = \frac{3}{4}

  5. Find the reciprocal by inverting the fraction.

    Reciprocal=134\text{Reciprocal} = \frac{1}{\frac{3}{4}}

  6. Simplify the expression.

    =43= \boxed{\frac{4}{3}}

    7. A school science club uses a value of 2.5×1032.5 \times 10^3 J of energy. Write this energy in ordinary form.

  7. Understand scientific notation.

    10310^3 means multiplying by 1000.

    2.5×103=2.5×10002.5 \times 10^3 = 2.5 \times 1000

  8. Perform the multiplication.

    =2500 J= \boxed{2500 \text{ J}}

    8. A digital thermometer records temperatures as integers. List any four consecutive integers between -3 and 3.

    The integers between -3 and 3 are -2, -1, 0, 1, 2.
    Four consecutive integers from this list are:

    −2,−1,0,1\boxed{-2, -1, 0, 1}
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