Matemática discreta Exemplos

$\frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 1

Multiplique $\frac{9}{10} \cdot \frac{9}{10}$ .

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Etapa 1.1

Multiplique $\frac{9}{10}$ por $\frac{9}{10}$ .

$\frac{9 \cdot 9}{10 \cdot 10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 1.2

Multiplique $9$ por $9$ .

$\frac{81}{10 \cdot 10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 1.3

Multiplique $10$ por $10$ .

$\frac{81}{100} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 2

Multiplique $\frac{81}{100} \cdot \frac{9}{10}$ .

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Etapa 2.1

Multiplique $\frac{81}{100}$ por $\frac{9}{10}$ .

$\frac{81 \cdot 9}{100 \cdot 10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 2.2

Multiplique $81$ por $9$ .

$\frac{729}{100 \cdot 10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 2.3

Multiplique $100$ por $10$ .

$\frac{729}{1000} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 3

Multiplique $\frac{729}{1000} \cdot \frac{9}{10}$ .

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Etapa 3.1

Multiplique $\frac{729}{1000}$ por $\frac{9}{10}$ .

$\frac{729 \cdot 9}{1000 \cdot 10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 3.2

Multiplique $729$ por $9$ .

$\frac{6561}{1000 \cdot 10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 3.3

Multiplique $1000$ por $10$ .

$\frac{6561}{10000} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 4

Multiplique $\frac{6561}{10000} \cdot \frac{9}{10}$ .

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Etapa 4.1

Multiplique $\frac{6561}{10000}$ por $\frac{9}{10}$ .

$\frac{6561 \cdot 9}{10000 \cdot 10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 4.2

Multiplique $6561$ por $9$ .

$\frac{59049}{10000 \cdot 10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 4.3

Multiplique $10000$ por $10$ .

$\frac{59049}{100000} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 5

Multiplique $\frac{59049}{100000} \cdot \frac{9}{10}$ .

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Etapa 5.1

Multiplique $\frac{59049}{100000}$ por $\frac{9}{10}$ .

$\frac{59049 \cdot 9}{100000 \cdot 10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 5.2

Multiplique $59049$ por $9$ .

$\frac{531441}{100000 \cdot 10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 5.3

Multiplique $100000$ por $10$ .

$\frac{531441}{1000000} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 6

Multiplique $\frac{531441}{1000000} \cdot \frac{9}{10}$ .

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Etapa 6.1

Multiplique $\frac{531441}{1000000}$ por $\frac{9}{10}$ .

$\frac{531441 \cdot 9}{1000000 \cdot 10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 6.2

Multiplique $531441$ por $9$ .

$\frac{4782969}{1000000 \cdot 10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 6.3

Multiplique $1000000$ por $10$ .

$\frac{4782969}{10000000} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 7

Multiplique $\frac{4782969}{10000000} \cdot \frac{9}{10}$ .

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Etapa 7.1

Multiplique $\frac{4782969}{10000000}$ por $\frac{9}{10}$ .

$\frac{4782969 \cdot 9}{10000000 \cdot 10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 7.2

Multiplique $4782969$ por $9$ .

$\frac{43046721}{10000000 \cdot 10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 7.3

Multiplique $10000000$ por $10$ .

$\frac{43046721}{100000000} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 8

Multiplique $\frac{43046721}{100000000} \cdot \frac{9}{10}$ .

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Etapa 8.1

Multiplique $\frac{43046721}{100000000}$ por $\frac{9}{10}$ .

$\frac{43046721 \cdot 9}{100000000 \cdot 10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 8.2

Multiplique $43046721$ por $9$ .

$\frac{387420489}{100000000 \cdot 10} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 8.3

Multiplique $100000000$ por $10$ .

$\frac{387420489}{1000000000} \cdot \frac{9}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 9

Multiplique $\frac{387420489}{1000000000} \cdot \frac{9}{10}$ .

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Etapa 9.1

Multiplique $\frac{387420489}{1000000000}$ por $\frac{9}{10}$ .

$\frac{387420489 \cdot 9}{1000000000 \cdot 10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 9.2

Multiplique $387420489$ por $9$ .

$\frac{3486784401}{1000000000 \cdot 10} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 9.3

Multiplique $1000000000$ por $10$ .

$\frac{3486784401}{10000000000} \cdot \frac{9}{10} \cdot \frac{9}{10}$

Etapa 10

Multiplique $\frac{3486784401}{10000000000} \cdot \frac{9}{10}$ .

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Etapa 10.1

Multiplique $\frac{3486784401}{10000000000}$ por $\frac{9}{10}$ .

$\frac{3486784401 \cdot 9}{10000000000 \cdot 10} \cdot \frac{9}{10}$

Etapa 10.2

Multiplique $3486784401$ por $9$ .

$\frac{31381059609}{10000000000 \cdot 10} \cdot \frac{9}{10}$

Etapa 10.3

Multiplique $10000000000$ por $10$ .

$\frac{31381059609}{100000000000} \cdot \frac{9}{10}$

Etapa 11

Multiplique $\frac{31381059609}{100000000000} \cdot \frac{9}{10}$ .

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Etapa 11.1

Multiplique $\frac{31381059609}{100000000000}$ por $\frac{9}{10}$ .

$\frac{31381059609 \cdot 9}{100000000000 \cdot 10}$

Etapa 11.2

Multiplique $31381059609$ por $9$ .

$\frac{282429536481}{100000000000 \cdot 10}$

Etapa 11.3

Multiplique $100000000000$ por $10$ .

$\frac{282429536481}{1000000000000}$

Etapa 12

O resultado pode ser mostrado de várias formas.

Forma exata:

$\frac{282429536481}{1000000000000}$

Forma decimal:

$0.28242953 \dots$