2 - Efotuo as operaçôes com notaçao ciontica: a) $$ 5 \cdot 10^{9} \cdot 2 \cdot 10^{13}= $$ b) $$ 9.10^{9}, 2.10^{-4} \cdot 0,5.10^{3}= $$ c) $$ 9.10^{9} \cdot 2 \cdot 10^{5} \cdot 12 \cdot 5 \cdot 10^{-6}= $$ d) $$ \left(9.10^{8}\right):\left(3,10^{-3}\right)= $$ o) $$ \left(9 \cdot 10^{18}\right):\left(2 \cdot 10^{12}\right)= $$ f) $$ \left(9,10^{3}: 18,10^{-3}\right), 0,5,10^{8}= $$ a) $$ 25.4 \cdot 10^{7}-12.3 \cdot 10^{3}= $$ h) $$ 0,23 \cdot 10^{-3}+0,4 \cdot 10^{-3}= $$

Question

UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(9\times 10^{8}\right)}{\left(3\times 10^{-3}\right)}$$
- step1: Evaluate:
  $$\frac{9\times 10^{8}}{3\times 10^{-3}}$$
- step2: Separate the fraction:
  $$\frac{9}{3}\times \frac{10^{8}}{10^{-3}}$$
- step3: Divide:
  $$3\times \frac{10^{8}}{10^{-3}}$$
- step4: Divide:
  $$3\times 10^{8-\left(-3\right)}$$
- step5: Evaluate:
  $$3\times 10^{11}$$
Calculate or simplify the expression $$ (9 * 10^{3}) / (18 * 10^{-3}) * 0.5 * 10^{8} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(9\times 10^{3}\right)}{\left(18\times 10^{-3}\right)}\times 0.5\times 10^{8}$$
- step1: Evaluate:
  $$\frac{9\times 10^{3}}{\left(18\times 10^{-3}\right)}\times 0.5\times 10^{8}$$
- step2: Remove the parentheses:
  $$\frac{9\times 10^{3}}{18\times 10^{-3}}\times 0.5\times 10^{8}$$
- step3: Reduce the fraction:
  $$10^{5}\times 5\times 0.5\times 10^{8}$$
- step4: Multiply the terms:
  $$5\times 10^{5}\times 0.5\times 10^{8}$$
- step5: Multiply the terms:
  $$2.5\times 10^{5}\times 10^{8}$$
- step6: Multiply the terms:
  $$2.5\times 10^{5+8}$$
- step7: Add the numbers:
  $$2.5\times 10^{13}$$
Calculate or simplify the expression $$ 0.23 * 10^{-3} + 0.4 * 10^{-3} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$0.23\times 10^{-3}+0.4\times 10^{-3}$$
- step1: Multiply the numbers:
  $$\frac{23}{10^{5}}+0.4\times 10^{-3}$$
- step2: Multiply the numbers:
  $$\frac{23}{10^{5}}+\frac{1}{2500}$$
- step3: Reduce fractions to a common denominator:
  $$\frac{23\times 2500}{10^{5}\times 2500}+\frac{10^{5}}{2500\times 10^{5}}$$
- step4: Reorder the terms:
  $$\frac{23\times 2500}{2500\times 10^{5}}+\frac{10^{5}}{2500\times 10^{5}}$$
- step5: Transform the expression:
  $$\frac{23\times 2500+10^{5}}{2500\times 10^{5}}$$
- step6: Multiply the numbers:
  $$\frac{57500+10^{5}}{2500\times 10^{5}}$$
- step7: Rewrite the expression:
  $$\frac{2500\left(23+40\right)}{2500\times 10^{5}}$$
- step8: Reduce the fraction:
  $$\frac{23+40}{10^{5}}$$
- step9: Simplify:
  $$\frac{63}{10^{5}}$$
Calculate or simplify the expression $$ 9 * 10^{9} * 2 * 10^{-4} * 0.5 * 10^{3} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$9\times 10^{9}\times 2\times 10^{-4}\times 0.5\times 10^{3}$$
- step1: Multiply the terms:
  $$9\times 10^{9}\times 10^{-4}\times 10^{3}$$
- step2: Multiply the terms:
  $$9\times 10^{9-4+3}$$
- step3: Calculate:
  $$9\times 10^{8}$$
Calculate or simplify the expression $$ 5 * 10^{9} * 2 * 10^{13} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$5\times 10^{9}\times 2\times 10^{13}$$
- step1: Multiply the numbers:
  $$10\times 10^{9}\times 10^{13}$$
- step2: Multiply:
  $$10\times 10^{22}$$
- step3: Multiply:
  $$10^{1+22}$$
- step4: Multiply the numbers:
  $$10^{23}$$
Calculate or simplify the expression $$ 25.4 * 10^{7} - 12.3 * 10^{3} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$25.4\times 10^{7}-12.3\times 10^{3}$$
- step1: Multiply the numbers:
  $$254000000-12.3\times 10^{3}$$
- step2: Multiply the numbers:
  $$254000000-12300$$
- step3: Subtract the numbers:
  $$253987700$$
Calculate or simplify the expression $$ (9 * 10^{18}) / (2 * 10^{12}) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{9\times 10^{18}}{2\times 10^{12}}$$
- step1: Separate the fraction:
  $$\frac{9}{2}\times \frac{10^{18}}{10^{12}}$$
- step2: Divide:
  $$4.5\times \frac{10^{18}}{10^{12}}$$
- step3: Divide:
  $$4.5\times 10^{18-12}$$
- step4: Evaluate:
  $$4.5\times 10^{6}$$
Calculate or simplify the expression $$ 9 * 10^{9} * 2 * 10^{5} * 12 * 5 * 10^{-6} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$9\times 10^{9}\times 2\times 10^{5}\times 12\times 5\times 10^{-6}$$
- step1: Multiply the terms:
  $$1080\times 10^{9}\times 10^{5}\times 10^{-6}$$
- step2: Multiply the terms:
  $$1080\times 10^{9+5-6}$$
- step3: Calculate:
  $$1080\times 10^{8}$$
Vamos resolver as operações com notação científica uma a uma:

a) $$ 5 \cdot 10^{9} \cdot 2 \cdot 10^{13} $$

Para resolver, multiplicamos os coeficientes e somamos os expoentes:

$$
5 \cdot 2 = 10
$$
$$
10^{9} \cdot 10^{13} = 10^{9 + 13} = 10^{22}
$$

Portanto, o resultado é:
$$
10^{23}
$$

---

b) $$ 9 \cdot 10^{9} \cdot 2 \cdot 10^{-4} \cdot 0,5 \cdot 10^{3} $$

Multiplicamos os coeficientes:

$$
9 \cdot 2 \cdot 0,5 = 9
$$

E somamos os expoentes:

$$
10^{9} \cdot 10^{-4} \cdot 10^{3} = 10^{9 - 4 + 3} = 10^{8}
$$

Portanto, o resultado é:
$$
9 \cdot 10^{8}
$$

---

c) $$ 9 \cdot 10^{9} \cdot 2 \cdot 10^{5} \cdot 12 \cdot 5 \cdot 10^{-6} $$

Multiplicamos os coeficientes:

$$
9 \cdot 2 \cdot 12 \cdot 5 = 1080
$$

E somamos os expoentes:

$$
10^{9} \cdot 10^{5} \cdot 10^{-6} = 10^{9 + 5 - 6} = 10^{8}
$$

Portanto, o resultado é:
$$
1080 \cdot 10^{8} \quad \text{ou} \quad 1.08 \cdot 10^{11}
$$

---

d) $$ \left(9 \cdot 10^{8}\right) : \left(3 \cdot 10^{-3}\right) $$

Dividimos os coeficientes:

$$
\frac{9}{3} = 3
$$

E subtraímos os expoentes:

$$
10^{8} / 10^{-3} = 10^{8 - (-3)} = 10^{8 + 3} = 10^{11}
$$

Portanto, o resultado é:
$$
3 \cdot 10^{11}
$$

---

e) $$ \left(9 \cdot 10^{18}\right) : \left(2 \cdot 10^{12}\right) $$

Dividimos os coeficientes:

$$
\frac{9}{2} = 4.5
$$

E subtraímos os expoentes:

$$
10^{18} / 10^{12} = 10^{18 - 12} = 10^{6}
$$

Portanto, o resultado é:
$$
4.5 \cdot 10^{6}
$$

---

f) $$ \left(9 \cdot 10^{3} : 18 \cdot 10^{-3}\right) \cdot 0,5 \cdot 10^{8} $$

Primeiro, resolvemos a divisão:

$$
\frac{9}{18} = 0.5
$$

E subtraímos os expoentes:

$$
10^{3} / 10^{-3} = 10^{3 - (-3)} = 10^{3 + 3} = 10^{6}
$$

Agora, multiplicamos:

$$
0.5 \cdot 0.5 = 0.25
$$
$$
0.25 \cdot 10^{6} = 2.5 \cdot 10^{5}
$$

Portanto, o resultado é:
$$
2.5 \cdot 10^{5}
$$

---

g) $$ 25.4 \cdot 10^{7} - 12.3 \cdot 10^{3} $$

Primeiro, precisamos expressar $$ 12.3 \cdot 10^{3} $$ na mesma ordem de grandeza que $$ 25.4 \cdot 10^{7} $$:

$$
12.3 \cdot 10^{3} = 0.00123 \cdot 10^{7}
$$

Agora, subtraímos:

$$
25.4 \cdot 10^{7} - 0.00123 \cdot 10^{7} = (25.4 - 0.00123) \cdot 10^{7} = 25.39877 \cdot 10^{7}
$$

Portanto, o resultado é:
$$
2.539877 \cdot 10^{8}
$$

---

h) $$ 0,23 \cdot 10^{-3} + 0,4 \cdot 10^{-3} $$

Somamos os coeficientes:

$$
0.23 + 0.4 = 0.63
$$

Portanto, o resultado é:
$$
0.63 \cdot 10^{-3} = 6.3 \cdot 10^{-4}
$$

---

Resumindo os resultados:

a) $$ 10^{23} $$

b) $$ 9 \cdot 10^{8} $$

c) $$ 1.08 \cdot 10^{11} $$

d) $$ 3 \cdot 10^{11} $$

e) $$ 4.5 \cdot 10^{6} $$

f) $$ 2.5 \cdot 10^{5} $$

g) $$ 2.539877 \cdot 10^{8} $$

h) $$ 6.3 \cdot 10^{-4} $$
a) $$ 10^{23} $$ b) $$ 9 \cdot 10^{8} $$ c) $$ 1.08 \cdot 10^{11} $$ d) $$ 3 \cdot 10^{11} $$ e) $$ 4.5 \cdot 10^{6} $$ f) $$ 2.5 \cdot 10^{5} $$ g) $$ 2.539877 \cdot 10^{8} $$ h) $$ 6.3 \cdot 10^{-4} $$

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