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Identify the dimensions of the rectangle.

Mathematics

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Step-by-step solution

6 steps

b.i)

  1. Identify the dimensions of the rectangle.

    Length (ll) = 0.003 m
    Width (ww) = 0.0024 m

  2. Calculate the perimeter.

    The formula for the perimeter of a rectangle is P=2(l+w)P = 2(l + w).

    P=2(0.003 m+0.0024 m)P = 2(0.003 \text{ m} + 0.0024 \text{ m}) P=2(0.0054 m)P = 2(0.0054 \text{ m}) P=0.0108 mP = 0.0108 \text{ m}
  3. Express the perimeter in standard form.

    Standard form is a×10na \times 10^n, where 1≤∣a∣<101 \le |a| < 10.
    To move the decimal point two places to the right to get 1.08, the exponent will be −2-2.

    P=1.08×10−2 mP = 1.08 \times 10^{-2} \text{ m}

    The perimeter in standard form is 1.08×10−2 m\boxed{\text{}1.08 \times 10^{-2} \text{ m}}.

    b.ii)

  4. Calculate the area.

    The formula for the area of a rectangle is A=l×wA = l \times w.

    A=0.003 m×0.0024 mA = 0.003 \text{ m} \times 0.0024 \text{ m}
  5. Convert the dimensions to standard form for multiplication.

    0.003=3×10−30.003 = 3 \times 10^{-3} 0.0024=2.4×10−30.0024 = 2.4 \times 10^{-3}
  6. Multiply the numbers in standard form.

    A=(3×10−3)×(2.4×10−3)A = (3 \times 10^{-3}) \times (2.4 \times 10^{-3}) A=(3×2.4)×(10−3×10−3)A = (3 \times 2.4) \times (10^{-3} \times 10^{-3}) A=7.2×10(−3−3)A = 7.2 \times 10^{(-3-3)} A=7.2×10−6 m2A = 7.2 \times 10^{-6} \text{ m}^2

    The area in standard form is 7.2×10−6 m2\boxed{\text{}7.2 \times 10^{-6} \text{ m}^2}.

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