Soalan 1:
Hitung nilai setiap operasi berikut. Nyatakan jawapan dalam bentuk piawai.
(a) 4 × 105 × 3.7 × 102
(b) 7.5 × 10−3 × 5 × 10−6
(c) 6.3 × 105 × 4.0 × 102
(d) 5.3 × 10−3 × 4 × 105
(e) (1.08 × 102) ÷ (2.4 × 104)
(f) (9.6 × 10−2) ÷ (1.5 × 10−5)
(g) (5.9 × 105) ÷ (2 × 102)
(h) (2.58 × 104) ÷ (0.3 × 10–4)
Penyelesaian:
(a)
$$ \begin{aligned} & 4 \times 10^5 \times 3.7 \times 10^2 \\ & =(4 \times 3.7) \times 10^{5+2} \\ & =14.8 \times 10^7 \\ & =1.48 \times 10^1 \times 10^7 \\ & =1.48 \times 10^{1+7} \\ & =1.48 \times 10^8 \end{aligned} $$
(b)
$$ \begin{aligned} & 7.5 \times 10^{-3} \times 5 \times 10^{-6} \\ & =(7.5 \times 5) \times 10^{-3+(-6)} \\ & =37.5 \times 10^{-9} \\ & =3.75 \times 10^1 \times 10^{-9} \\ & =3.75 \times 10^{1-9} \\ & =3.75 \times 10^{-8} \end{aligned} $$
(c)
$$ \begin{aligned} & 6.3 \times 10^5 \times 4.0 \times 10^2 \\ & =(6.3 \times 4.0) \times 10^{5+2} \\ & =25.2 \times 10^7 \\ & =2.52 \times 10^1 \times 10^7 \\ & =2.52 \times 10^{1+7} \\ & =2.52 \times 10^8 \end{aligned} $$
(d)
$$ \begin{aligned} & 5.3 \times 10^{-3} \times 4 \times 10^5 \\ & =(5.3 \times 4) \times 10^{-3+5} \\ & =21.2 \times 10^2 \\ & =2.12 \times 10^1 \times 10^2 \\ & =2.12 \times 10^{1+2} \\ & =2.12 \times 10^3 \end{aligned} $$
(e)
$$ \begin{aligned} & \left(1.08 \times 10^2\right) \div\left(2.4 \times 10^4\right) \\ & =\frac{1.08}{2.4} \times 10^{2-4} \\ & =0.45 \times 10^{-2} \\ & =4.5 \times 10^{-1} \times 10^{-2} \\ & =4.5 \times 10^{-3} \end{aligned} $$
(f)
$$ \begin{aligned} & \left(9.6 \times 10^{-2}\right) \div\left(1.5 \times 10^{-5}\right) \\ & =\frac{9.6}{1.5} \times 10^{-2-5} \\ & =6.4 \times 10^{-7} \end{aligned} $$
(g)
$$ \begin{aligned} & \left(5.9 \times 10^5\right) \div\left(2 \times 10^2\right) \\ & =\frac{5.9}{2} \times 10^{5-2} \\ & =2.95 \times 10^3 \end{aligned} $$
(h)
$$ \begin{aligned} & \left(2.58 \times 10^4\right) \div\left(0.3 \times 10^{-4}\right) \\ & =\frac{2.58}{0.3} \times 10^{4-(-4)} \\ & =8.6 \times 10^{4+4} \\ & =8.6 \times 10^8 \end{aligned} $$
Hitung nilai setiap operasi berikut. Nyatakan jawapan dalam bentuk piawai.
(a) 4 × 105 × 3.7 × 102
(b) 7.5 × 10−3 × 5 × 10−6
(c) 6.3 × 105 × 4.0 × 102
(d) 5.3 × 10−3 × 4 × 105
(e) (1.08 × 102) ÷ (2.4 × 104)
(f) (9.6 × 10−2) ÷ (1.5 × 10−5)
(g) (5.9 × 105) ÷ (2 × 102)
(h) (2.58 × 104) ÷ (0.3 × 10–4)
Penyelesaian:
(a)
$$ \begin{aligned} & 4 \times 10^5 \times 3.7 \times 10^2 \\ & =(4 \times 3.7) \times 10^{5+2} \\ & =14.8 \times 10^7 \\ & =1.48 \times 10^1 \times 10^7 \\ & =1.48 \times 10^{1+7} \\ & =1.48 \times 10^8 \end{aligned} $$
(b)
$$ \begin{aligned} & 7.5 \times 10^{-3} \times 5 \times 10^{-6} \\ & =(7.5 \times 5) \times 10^{-3+(-6)} \\ & =37.5 \times 10^{-9} \\ & =3.75 \times 10^1 \times 10^{-9} \\ & =3.75 \times 10^{1-9} \\ & =3.75 \times 10^{-8} \end{aligned} $$
(c)
$$ \begin{aligned} & 6.3 \times 10^5 \times 4.0 \times 10^2 \\ & =(6.3 \times 4.0) \times 10^{5+2} \\ & =25.2 \times 10^7 \\ & =2.52 \times 10^1 \times 10^7 \\ & =2.52 \times 10^{1+7} \\ & =2.52 \times 10^8 \end{aligned} $$
(d)
$$ \begin{aligned} & 5.3 \times 10^{-3} \times 4 \times 10^5 \\ & =(5.3 \times 4) \times 10^{-3+5} \\ & =21.2 \times 10^2 \\ & =2.12 \times 10^1 \times 10^2 \\ & =2.12 \times 10^{1+2} \\ & =2.12 \times 10^3 \end{aligned} $$
(e)
$$ \begin{aligned} & \left(1.08 \times 10^2\right) \div\left(2.4 \times 10^4\right) \\ & =\frac{1.08}{2.4} \times 10^{2-4} \\ & =0.45 \times 10^{-2} \\ & =4.5 \times 10^{-1} \times 10^{-2} \\ & =4.5 \times 10^{-3} \end{aligned} $$
(f)
$$ \begin{aligned} & \left(9.6 \times 10^{-2}\right) \div\left(1.5 \times 10^{-5}\right) \\ & =\frac{9.6}{1.5} \times 10^{-2-5} \\ & =6.4 \times 10^{-7} \end{aligned} $$
(g)
$$ \begin{aligned} & \left(5.9 \times 10^5\right) \div\left(2 \times 10^2\right) \\ & =\frac{5.9}{2} \times 10^{5-2} \\ & =2.95 \times 10^3 \end{aligned} $$
(h)
$$ \begin{aligned} & \left(2.58 \times 10^4\right) \div\left(0.3 \times 10^{-4}\right) \\ & =\frac{2.58}{0.3} \times 10^{4-(-4)} \\ & =8.6 \times 10^{4+4} \\ & =8.6 \times 10^8 \end{aligned} $$