Matematica di base Esempi

$4.44 = 10 (1 - 0.5 \cdot 10^{- 3} + 0.5 \cdot 10^{- 6}) \cdot u$

Passaggio 1

Riscrivi l'equazione come $10 (1 - 0.5 \cdot 10^{- 3} + 0.5 \cdot 10^{- 6}) \cdot u = 4.44$ .

$10 (1 - 0.5 \cdot 10^{- 3} + 0.5 \cdot 10^{- 6}) \cdot u = 4.44$

Passaggio 2

Semplifica.

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Passaggio 2.1

Move the decimal point in $- 0.5$ to the right by $1$ place and decrease the power of $10^{- 3}$ by $1$ .

$10 (1 - 5 \cdot 10^{- 4} + 0.5 \cdot 10^{- 6}) \cdot u = 4.44$

Passaggio 2.2

Move the decimal point in $0.5$ to the right by $1$ place and decrease the power of $10^{- 6}$ by $1$ .

$10 (1 - 5 \cdot 10^{- 4} + 5 \cdot 10^{- 7}) \cdot u = 4.44$

Passaggio 2.3

Applica la proprietà distributiva.

$(10 \cdot 1 + 10 \cdot - 5 \cdot 10^{- 4} + 10 \cdot 5 \cdot 10^{- 7}) \cdot u = 4.44$

Passaggio 2.4

Semplifica.

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Passaggio 2.4.1

Moltiplica $10$ per $1$ .

$(10 + 10 \cdot - 5 \cdot 10^{- 4} + 10 \cdot 5 \cdot 10^{- 7}) \cdot u = 4.44$

Passaggio 2.4.2

Moltiplica $10$ per $- 5$ .

$(10 - 50 \cdot 10^{- 4} + 10 \cdot 5 \cdot 10^{- 7}) \cdot u = 4.44$

Passaggio 2.4.3

Moltiplica $10$ per $5$ .

$(10 - 50 \cdot 10^{- 4} + 50 \cdot 10^{- 7}) \cdot u = 4.44$

Passaggio 2.5

Move the decimal point in $- 50$ to the left by $1$ place and increase the power of $10^{- 4}$ by $1$ .

$(10 - 5 \cdot 10^{- 3} + 50 \cdot 10^{- 7}) \cdot u = 4.44$

Passaggio 2.6

Move the decimal point in $50$ to the left by $1$ place and increase the power of $10^{- 7}$ by $1$ .

$(10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}) \cdot u = 4.44$

Passaggio 3

Dividi per $10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}$ ciascun termine in $(10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}) \cdot u = 4.44$ e semplifica.

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Passaggio 3.1

Dividi per $10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}$ ciascun termine in $(10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}) \cdot u = 4.44$ .

$\frac{(10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}) \cdot u}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2

Semplifica il lato sinistro.

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Passaggio 3.2.1

Convert $10$ to scientific notation.

$\frac{(1 \cdot 10^{1} - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}) \cdot u}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2.2

Move the decimal point in $- 5$ to the left by $4$ places and increase the power of $10^{- 3}$ by $4$ .

$\frac{(1 \cdot 10^{1} - 0.0005 \cdot 10^{1} + 5 \cdot 10^{- 6}) \cdot u}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2.3

Scomponi $10^{1}$ da $1 \cdot 10^{1} - 0.0005 \cdot 10^{1}$ .

$\frac{((1 - 0.0005) \cdot 10^{1} + 5 \cdot 10^{- 6}) \cdot u}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2.4

Sottrai $0.0005$ da $1$ .

$\frac{(0.9995 \cdot 10^{1} + 5 \cdot 10^{- 6}) \cdot u}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2.5

Move the decimal point in $0.9995$ to the right by $1$ place and decrease the power of $10^{1}$ by $1$ .

$\frac{(9.995 \cdot 10^{0} + 5 \cdot 10^{- 6}) \cdot u}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2.6

Move the decimal point in $5$ to the left by $6$ places and increase the power of $10^{- 6}$ by $6$ .

$\frac{(9.995 \cdot 10^{0} + 0.000005 \cdot 10^{0}) \cdot u}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2.7

Scomponi $10^{0}$ da $9.995 \cdot 10^{0} + 0.000005 \cdot 10^{0}$ .

$\frac{(9.995 + 0.000005) \cdot 10^{0} \cdot u}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2.8

Somma $9.995$ e $0.000005$ .

$\frac{9.995005 \cdot 10^{0} \cdot u}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2.9

Convert $10$ to scientific notation.

$\frac{9.995005 \cdot 10^{0} \cdot u}{1 \cdot 10^{1} - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2.10

Move the decimal point in $- 5$ to the left by $4$ places and increase the power of $10^{- 3}$ by $4$ .

$\frac{9.995005 \cdot 10^{0} \cdot u}{1 \cdot 10^{1} - 0.0005 \cdot 10^{1} + 5 \cdot 10^{- 6}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2.11

Scomponi $10^{1}$ da $1 \cdot 10^{1} - 0.0005 \cdot 10^{1}$ .

$\frac{9.995005 \cdot 10^{0} \cdot u}{(1 - 0.0005) \cdot 10^{1} + 5 \cdot 10^{- 6}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2.12

Sottrai $0.0005$ da $1$ .

$\frac{9.995005 \cdot 10^{0} \cdot u}{0.9995 \cdot 10^{1} + 5 \cdot 10^{- 6}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2.13

Move the decimal point in $0.9995$ to the right by $1$ place and decrease the power of $10^{1}$ by $1$ .

$\frac{9.995005 \cdot 10^{0} \cdot u}{9.995 \cdot 10^{0} + 5 \cdot 10^{- 6}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2.14

Move the decimal point in $5$ to the left by $6$ places and increase the power of $10^{- 6}$ by $6$ .

$\frac{9.995005 \cdot 10^{0} \cdot u}{9.995 \cdot 10^{0} + 0.000005 \cdot 10^{0}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2.15

Scomponi $10^{0}$ da $9.995 \cdot 10^{0} + 0.000005 \cdot 10^{0}$ .

$\frac{9.995005 \cdot 10^{0} \cdot u}{(9.995 + 0.000005) \cdot 10^{0}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2.16

Somma $9.995$ e $0.000005$ .

$\frac{9.995005 \cdot 10^{0} \cdot u}{9.995005 \cdot 10^{0}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2.17

Elimina il fattore comune di $9.995005$ .

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Passaggio 3.2.17.1

Elimina il fattore comune.

$\frac{9.995005 \cdot 10^{0} \cdot u}{9.995005 \cdot 10^{0}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2.17.2

Riscrivi l'espressione.

$\frac{10^{0} \cdot u}{10^{0}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2.18

Elimina il fattore comune di $10^{0}$ .

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Passaggio 3.2.18.1

Elimina il fattore comune.

$\frac{10^{0} \cdot u}{10^{0}} = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.2.18.2

Dividi $u$ per $1$ .

$u = \frac{4.44}{10 - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.3

Semplifica il lato destro.

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Passaggio 3.3.1

Convert $10$ to scientific notation.

$u = \frac{4.44}{1 \cdot 10^{1} - 5 \cdot 10^{- 3} + 5 \cdot 10^{- 6}}$

Passaggio 3.3.2

Move the decimal point in $- 5$ to the left by $4$ places and increase the power of $10^{- 3}$ by $4$ .

$u = \frac{4.44}{1 \cdot 10^{1} - 0.0005 \cdot 10^{1} + 5 \cdot 10^{- 6}}$

Passaggio 3.3.3

Scomponi $10^{1}$ da $1 \cdot 10^{1} - 0.0005 \cdot 10^{1}$ .

$u = \frac{4.44}{(1 - 0.0005) \cdot 10^{1} + 5 \cdot 10^{- 6}}$

Passaggio 3.3.4

Sottrai $0.0005$ da $1$ .

$u = \frac{4.44}{0.9995 \cdot 10^{1} + 5 \cdot 10^{- 6}}$

Passaggio 3.3.5

Move the decimal point in $0.9995$ to the right by $1$ place and decrease the power of $10^{1}$ by $1$ .

$u = \frac{4.44}{9.995 \cdot 10^{0} + 5 \cdot 10^{- 6}}$

Passaggio 3.3.6

Move the decimal point in $5$ to the left by $6$ places and increase the power of $10^{- 6}$ by $6$ .

$u = \frac{4.44}{9.995 \cdot 10^{0} + 0.000005 \cdot 10^{0}}$

Passaggio 3.3.7

Scomponi $10^{0}$ da $9.995 \cdot 10^{0} + 0.000005 \cdot 10^{0}$ .

$u = \frac{4.44}{(9.995 + 0.000005) \cdot 10^{0}}$

Passaggio 3.3.8

Somma $9.995$ e $0.000005$ .

$u = \frac{4.44}{9.995005 \cdot 10^{0}}$

Passaggio 3.3.9

Dividi usando la notazione scientifica.

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Passaggio 3.3.9.1

Raggruppa separatamente i coefficienti e gli esponenti per dividere i numeri in notazione scientifica.

$u = (\frac{4.44}{9.995005}) (\frac{1}{10^{0}})$

Passaggio 3.3.9.2

Dividi $4.44$ per $9.995005$ .

$u = 0.44422188 \frac{1}{10^{0}}$

Passaggio 3.3.9.3

Sposta $10^{0}$ al numeratore usando la regola dell'esponente negativo $\frac{1}{b^{- n}} = b^{n}$ .

$u = 0.44422188 \cdot 10^{0}$

Passaggio 3.3.10

Move the decimal point in $0.44422188$ to the right by $1$ place and decrease the power of $10^{0}$ by $1$ .

$u = 4.44221888 \cdot 10^{- 1}$

Passaggio 4

Il risultato può essere mostrato in più forme.

Notazione scientifica:

$u = 4.44221888 \cdot 10^{- 1}$

Forma estesa:

$u = 0.44422188$