Ratkaise 5000*1/8%*(1-1/108^30)

$$5000 \times \frac { 1 } { 8 \% } \times ( 1 - \frac { 1 } { 108 ^ { 30 } } )$$

Laske

$$\frac{157229013891772345498599951736092754417390325814062078754815984375}{2515664222268357527977599227777484070678245213024993260077056}\approx 62500$$

Ratkaisun vaiheet

Jaa 1 luvulla \frac{8}{100} kertomalla 1 luvun \frac{8}{100} käänteisluvulla.

$$5000\times \frac{100}{8}\left(1-\frac{1}{108^{30}}\right)$$

Supista murtoluku \frac{100}{8} luvulla 4.

$$5000\times \frac{25}{2}\left(1-\frac{1}{108^{30}}\right)$$

Ilmaise 5000\times \frac{25}{2} säännöllisenä murtolukuna.

$$\frac{5000\times 25}{2}\left(1-\frac{1}{108^{30}}\right)$$

Kerro 5000 ja 25, niin saadaan 125000.

$$\frac{125000}{2}\left(1-\frac{1}{108^{30}}\right)$$

Jaa 125000 luvulla 2, jolloin ratkaisuksi tulee 62500.

$$62500\left(1-\frac{1}{108^{30}}\right)$$

Laske 108 potenssiin 30, jolloin ratkaisuksi tulee 10062656889073430111910396911109936282712980852099973040308224.

$$62500\left(1-\frac{1}{10062656889073430111910396911109936282712980852099973040308224}\right)$$

Muunna 1 murtoluvuksi \frac{10062656889073430111910396911109936282712980852099973040308224}{10062656889073430111910396911109936282712980852099973040308224}.

$$62500\left(\frac{10062656889073430111910396911109936282712980852099973040308224}{10062656889073430111910396911109936282712980852099973040308224}-\frac{1}{10062656889073430111910396911109936282712980852099973040308224}\right)$$

Koska arvoilla \frac{10062656889073430111910396911109936282712980852099973040308224}{10062656889073430111910396911109936282712980852099973040308224} ja \frac{1}{10062656889073430111910396911109936282712980852099973040308224} on sama nimittäjä, laske niiden erotus vähentämällä niiden osoittajat toisistaan.

$$62500\times \frac{10062656889073430111910396911109936282712980852099973040308224-1}{10062656889073430111910396911109936282712980852099973040308224}$$

Vähennä 1 luvusta 10062656889073430111910396911109936282712980852099973040308224 saadaksesi tuloksen 10062656889073430111910396911109936282712980852099973040308223.

$$62500\times \frac{10062656889073430111910396911109936282712980852099973040308223}{10062656889073430111910396911109936282712980852099973040308224}$$

Ilmaise 62500\times \frac{10062656889073430111910396911109936282712980852099973040308223}{10062656889073430111910396911109936282712980852099973040308224} säännöllisenä murtolukuna.

$$\frac{62500\times 10062656889073430111910396911109936282712980852099973040308223}{10062656889073430111910396911109936282712980852099973040308224}$$

Kerro 62500 ja 10062656889073430111910396911109936282712980852099973040308223, niin saadaan 628916055567089381994399806944371017669561303256248315019263937500.

$$\frac{628916055567089381994399806944371017669561303256248315019263937500}{10062656889073430111910396911109936282712980852099973040308224}$$

Supista murtoluku \frac{628916055567089381994399806944371017669561303256248315019263937500}{10062656889073430111910396911109936282712980852099973040308224} luvulla 4.

$$\frac{157229013891772345498599951736092754417390325814062078754815984375}{2515664222268357527977599227777484070678245213024993260077056}$$