Whakaoti i te 991/9100/9999/999999/100frac{101}{99}

$$99 \frac { 1 } { 9 } \frac { 100 } { 99 } \frac { 99 } { 99 } 99 \frac { 99 } { 100 } \frac { 101 } { 99 }$$

Aromātai

$$\frac{9099292}{891}\approx 10212.448933782$$

Ngā Upane Otinga

Whakawehea te 99 ki te 99, kia riro ko 1.

$$\frac{99\times 9+1}{9}\times \frac{100}{99}\times 1\times \frac{99\times 100+99}{100}\times \frac{101}{99}$$

Whakareatia te 99 ki te 9, ka 891.

$$\frac{891+1}{9}\times \frac{100}{99}\times 1\times \frac{99\times 100+99}{100}\times \frac{101}{99}$$

Tāpirihia te 891 ki te 1, ka 892.

$$\frac{892}{9}\times \frac{100}{99}\times 1\times \frac{99\times 100+99}{100}\times \frac{101}{99}$$

Me whakarea te \frac{892}{9} ki te \frac{100}{99} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{892\times 100}{9\times 99}\times 1\times \frac{99\times 100+99}{100}\times \frac{101}{99}$$

Mahia ngā whakarea i roto i te hautanga \frac{892\times 100}{9\times 99}.

$$\frac{89200}{891}\times 1\times \frac{99\times 100+99}{100}\times \frac{101}{99}$$

Whakareatia te \frac{89200}{891} ki te 1, ka \frac{89200}{891}.

$$\frac{89200}{891}\times \frac{99\times 100+99}{100}\times \frac{101}{99}$$

Whakareatia te 99 ki te 100, ka 9900.

$$\frac{89200}{891}\times \frac{9900+99}{100}\times \frac{101}{99}$$

Tāpirihia te 9900 ki te 99, ka 9999.

$$\frac{89200}{891}\times \frac{9999}{100}\times \frac{101}{99}$$

Me whakarea te \frac{89200}{891} ki te \frac{9999}{100} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{89200\times 9999}{891\times 100}\times \frac{101}{99}$$

Mahia ngā whakarea i roto i te hautanga \frac{89200\times 9999}{891\times 100}.

$$\frac{891910800}{89100}\times \frac{101}{99}$$

Whakahekea te hautanga \frac{891910800}{89100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 9900.

$$\frac{90092}{9}\times \frac{101}{99}$$

Me whakarea te \frac{90092}{9} ki te \frac{101}{99} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{90092\times 101}{9\times 99}$$

Mahia ngā whakarea i roto i te hautanga \frac{90092\times 101}{9\times 99}.

$$\frac{9099292}{891}$$

Tauwehe

$$\frac{2 ^ {2} \cdot 101 ^ {2} \cdot 223}{3 ^ {4} \cdot 11} = 10212\frac{400}{891} = 10212.448933782267$$