Réponse :
Explications étape par étape
Bonjour
On sait que
Donc
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Réponse :
Explications étape par étape
Bonjour
On sait que![10^{334} = 100^{333} \times 10 10^{334} = 100^{333} \times 10](https://tex.z-dn.net/?f=10%5E%7B334%7D%20%3D%20100%5E%7B333%7D%20%5Ctimes%2010)
Donc![C=\dfrac{1}{10^{333} } - \dfrac{1}{10^{334} } = \dfrac{1}{10^{333} } -\dfrac{1}{10^{333} \times 10} =\dfrac{1}{10^{333} } \left(1-\dfrac{1}{10}\right)\\\phantom{C}=\dfrac{1}{10^{333} } \times \dfrac{9}{10} =\dfrac{9}{10^{334} } \text{ ou } 9\times 10^{-334} C=\dfrac{1}{10^{333} } - \dfrac{1}{10^{334} } = \dfrac{1}{10^{333} } -\dfrac{1}{10^{333} \times 10} =\dfrac{1}{10^{333} } \left(1-\dfrac{1}{10}\right)\\\phantom{C}=\dfrac{1}{10^{333} } \times \dfrac{9}{10} =\dfrac{9}{10^{334} } \text{ ou } 9\times 10^{-334}](https://tex.z-dn.net/?f=C%3D%5Cdfrac%7B1%7D%7B10%5E%7B333%7D%20%7D%20-%20%5Cdfrac%7B1%7D%7B10%5E%7B334%7D%20%7D%20%3D%20%5Cdfrac%7B1%7D%7B10%5E%7B333%7D%20%7D%20-%5Cdfrac%7B1%7D%7B10%5E%7B333%7D%20%5Ctimes%2010%7D%20%3D%5Cdfrac%7B1%7D%7B10%5E%7B333%7D%20%7D%20%5Cleft%281-%5Cdfrac%7B1%7D%7B10%7D%5Cright%29%5C%5C%5Cphantom%7BC%7D%3D%5Cdfrac%7B1%7D%7B10%5E%7B333%7D%20%7D%20%5Ctimes%20%5Cdfrac%7B9%7D%7B10%7D%20%3D%5Cdfrac%7B9%7D%7B10%5E%7B334%7D%20%7D%20%5Ctext%7B%20ou%20%7D%209%5Ctimes%2010%5E%7B-334%7D)