Soalan 1:
Hitung nilai setiap operasi berikut. Nyatakan jawapan dalam bentuk
piawai.
(a) 2.4 × 104 + 3.57 × 104
(b) 8.2 × 106 – 4.27 × 106
(c) 5.23 × 107 + 4.98 × 107
(d) 1.2 × 105 + 3.74 × 104
(e) 5.7 × 108 – 2.4 × 107
(f) 5.7 × 103 + 8.02 × 104
(g) 6.5 × 104 − 7.3 × 103
(h) 5.2 × 10−3 − 4.12 × 10−3
(i) 8.74 × 10–5 – 2.65 × 10–5
(j) 4.1 × 10−4 + 9.5 × 10−3
(k) 8.3 × 10−4 − 6.2 × 10–5
(l) 9.42 × 10– 6 – 7.35 × 10−7
Penyelesaian:
(a)
$$ \begin{aligned} & 2.4 \times 10^4+3.57 \times 10^4 \\ & =(2.4+3.57) \times 10^4 \\ & =5.97 \times 10^4 \end{aligned} $$
(b)
$$ \begin{aligned} & 8.2 \times 10^6-4.27 \times 10^6 \\ & =(8.2-4.27) \times 10^6 \\ & =3.93 \times 10^6 \end{aligned} $$
(c)
$$ \begin{aligned} & 5.23 \times 10^7+4.98 \times 10^7 \\ & =(5.23+4.98) \times 10^7 \\ & =10.21 \times 10^7 \\ & =1.021 \times 10^1 \times 10^7 \\ & =1.021 \times 10^{1+7} \\ & =1.021 \times 10^8 \end{aligned} $$
(d)
$$ \begin{aligned} & 1.2 \times 10^5+3.74 \times 10^4 \\ & =1.2 \times 10^1 \times 10^4+3.74 \times 10^4 \\ & =12 \times 10^4+3.74 \times 10^4 \\ & =(12+3.74) \times 10^4 \\ & =15.74 \times 10^4 \\ & =1.574 \times 10^1 \times 10^4 \\ & =1.574 \times 10^{1+4} \\ & =1.574 \times 10^5 \end{aligned} $$
(e)
$$ \begin{aligned} & 5.7 \times 10^8-2.4 \times 10^7 \\ & =5.7 \times 10^1 \times 10^7-2.4 \times 10^7 \\ & =57 \times 10^7-2.4 \times 10^7 \\ & =(57-2.4) \times 10^7 \\ & =54.6 \times 10^7 \\ & =5.46 \times 10^1 \times 10^7 \\ & =5.46 \times 10^{1+7} \\ & =5.46 \times 10^8 \end{aligned} $$
(f)
$$ \begin{aligned} & 5.7 \times 10^3+8.02 \times 10^4 \\ & =5.7 \times 10^3+8.02 \times 10^1 \times 10^3 \\ & =5.7 \times 10^3+80.2 \times 10^3 \\ & =(5.7+80.2) \times 10^3 \\ & =85.9 \times 10^3 \\ & =8.59 \times 10^1 \times 10^3 \\ & =8.59 \times 10^{1+3} \\ & =8.59 \times 10^4 \end{aligned} $$
(g)
$$ \begin{aligned} & 6.5 \times 10^4-7.3 \times 10^3 \\ & =6.5 \times 10^4-7.3 \times 10^{-1} \times 10^4 \\ & =6.5 \times 10^4-0.73 \times 10^4 \\ & =(6.5-0.73) \times 10^4 \\ & =5.77 \times 10^4 \end{aligned} $$
(h)
$$ \begin{aligned} & 5.2 \times 10^{-3}-4.12 \times 10^{-3} \\ & =(5.2-4.12) \times 10^{-3} \\ & =1.08 \times 10^{-3} \end{aligned} $$
(i)
$$ \begin{aligned} & 8.74 \times 10^{-5}-2.65 \times 10^{-5} \\ & =(8.74-2.65) \times 10^{-5} \\ & =6.09 \times 10^{-5} \end{aligned} $$
(j)
$$ \begin{aligned} & 4.1 \times 10^{-4}+9.5 \times 10^{-3} \\ & =4.1 \times 10^{-1} \times 10^{-3}+9.5 \times 10^{-3} \\ & =0.41 \times 10^{-3}+9.5 \times 10^{-3} \\ & =(0.41+9.5) \times 10^{-3} \\ & =9.91 \times 10^{-3} \end{aligned} $$
(k)
$$ \begin{aligned} & 8.3 \times 10^{-4}-6.2 \times 10^{-5} \\ & =8.3 \times 10^{-4}-6.2 \times 10^{-1} \times 10^{-4} \\ & =8.3 \times 10^{-4}-0.62 \times 10^{-4} \\ & =(8.3-0.62) \times 10^{-4} \\ & =7.68 \times 10^{-4} \end{aligned} $$
(l)
$$ \begin{aligned} & 9.42 \times 10^{-6}-7.35 \times 10^{-7} \\ & =9.42 \times 10^{-6}-7.35 \times 10^{-1} \times 10^{-6} \\ & =9.42 \times 10^{-6}-0.735 \times 10^{-6} \\ & =(9.42-0.735) \times 10^{-6} \\ & =8.685 \times 10^{-6} \end{aligned} $$
Hitung nilai setiap operasi berikut. Nyatakan jawapan dalam bentuk
piawai.
(a) 2.4 × 104 + 3.57 × 104
(b) 8.2 × 106 – 4.27 × 106
(c) 5.23 × 107 + 4.98 × 107
(d) 1.2 × 105 + 3.74 × 104
(e) 5.7 × 108 – 2.4 × 107
(f) 5.7 × 103 + 8.02 × 104
(g) 6.5 × 104 − 7.3 × 103
(h) 5.2 × 10−3 − 4.12 × 10−3
(i) 8.74 × 10–5 – 2.65 × 10–5
(j) 4.1 × 10−4 + 9.5 × 10−3
(k) 8.3 × 10−4 − 6.2 × 10–5
(l) 9.42 × 10– 6 – 7.35 × 10−7
Penyelesaian:
(a)
$$ \begin{aligned} & 2.4 \times 10^4+3.57 \times 10^4 \\ & =(2.4+3.57) \times 10^4 \\ & =5.97 \times 10^4 \end{aligned} $$
(b)
$$ \begin{aligned} & 8.2 \times 10^6-4.27 \times 10^6 \\ & =(8.2-4.27) \times 10^6 \\ & =3.93 \times 10^6 \end{aligned} $$
(c)
$$ \begin{aligned} & 5.23 \times 10^7+4.98 \times 10^7 \\ & =(5.23+4.98) \times 10^7 \\ & =10.21 \times 10^7 \\ & =1.021 \times 10^1 \times 10^7 \\ & =1.021 \times 10^{1+7} \\ & =1.021 \times 10^8 \end{aligned} $$
(d)
$$ \begin{aligned} & 1.2 \times 10^5+3.74 \times 10^4 \\ & =1.2 \times 10^1 \times 10^4+3.74 \times 10^4 \\ & =12 \times 10^4+3.74 \times 10^4 \\ & =(12+3.74) \times 10^4 \\ & =15.74 \times 10^4 \\ & =1.574 \times 10^1 \times 10^4 \\ & =1.574 \times 10^{1+4} \\ & =1.574 \times 10^5 \end{aligned} $$
(e)
$$ \begin{aligned} & 5.7 \times 10^8-2.4 \times 10^7 \\ & =5.7 \times 10^1 \times 10^7-2.4 \times 10^7 \\ & =57 \times 10^7-2.4 \times 10^7 \\ & =(57-2.4) \times 10^7 \\ & =54.6 \times 10^7 \\ & =5.46 \times 10^1 \times 10^7 \\ & =5.46 \times 10^{1+7} \\ & =5.46 \times 10^8 \end{aligned} $$
(f)
$$ \begin{aligned} & 5.7 \times 10^3+8.02 \times 10^4 \\ & =5.7 \times 10^3+8.02 \times 10^1 \times 10^3 \\ & =5.7 \times 10^3+80.2 \times 10^3 \\ & =(5.7+80.2) \times 10^3 \\ & =85.9 \times 10^3 \\ & =8.59 \times 10^1 \times 10^3 \\ & =8.59 \times 10^{1+3} \\ & =8.59 \times 10^4 \end{aligned} $$
(g)
$$ \begin{aligned} & 6.5 \times 10^4-7.3 \times 10^3 \\ & =6.5 \times 10^4-7.3 \times 10^{-1} \times 10^4 \\ & =6.5 \times 10^4-0.73 \times 10^4 \\ & =(6.5-0.73) \times 10^4 \\ & =5.77 \times 10^4 \end{aligned} $$
(h)
$$ \begin{aligned} & 5.2 \times 10^{-3}-4.12 \times 10^{-3} \\ & =(5.2-4.12) \times 10^{-3} \\ & =1.08 \times 10^{-3} \end{aligned} $$
(i)
$$ \begin{aligned} & 8.74 \times 10^{-5}-2.65 \times 10^{-5} \\ & =(8.74-2.65) \times 10^{-5} \\ & =6.09 \times 10^{-5} \end{aligned} $$
(j)
$$ \begin{aligned} & 4.1 \times 10^{-4}+9.5 \times 10^{-3} \\ & =4.1 \times 10^{-1} \times 10^{-3}+9.5 \times 10^{-3} \\ & =0.41 \times 10^{-3}+9.5 \times 10^{-3} \\ & =(0.41+9.5) \times 10^{-3} \\ & =9.91 \times 10^{-3} \end{aligned} $$
(k)
$$ \begin{aligned} & 8.3 \times 10^{-4}-6.2 \times 10^{-5} \\ & =8.3 \times 10^{-4}-6.2 \times 10^{-1} \times 10^{-4} \\ & =8.3 \times 10^{-4}-0.62 \times 10^{-4} \\ & =(8.3-0.62) \times 10^{-4} \\ & =7.68 \times 10^{-4} \end{aligned} $$
(l)
$$ \begin{aligned} & 9.42 \times 10^{-6}-7.35 \times 10^{-7} \\ & =9.42 \times 10^{-6}-7.35 \times 10^{-1} \times 10^{-6} \\ & =9.42 \times 10^{-6}-0.735 \times 10^{-6} \\ & =(9.42-0.735) \times 10^{-6} \\ & =8.685 \times 10^{-6} \end{aligned} $$