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Completa para que se verifique la igualdad \( 6 \cdot 10^{7}+5 \cdot 10 \square+3 \cdot 10^{2}+2 \cdot 10^{0}=60050302 \)

Ask by Gough Rodriquez. in Argentina
Mar 14,2025

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Para que la igualdad \( 6 \cdot 10^{7} + 5 \cdot 10^{\square} + 3 \cdot 10^{2} + 2 \cdot 10^{0} = 60050302 \) se verifique, el valor de \(\square\) debe ser **4**.

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Para verificar la igualdad, primero evaluamos los términos que ya tenemos: - \(6 \cdot 10^{7} = 60000000\) - \(5 \cdot 10^{1} = 50\) (este es el término que debemos hallar) - \(3 \cdot 10^{2} = 300\) - \(2 \cdot 10^{0} = 2\) Ahora sumamos los valores que ya tenemos: \[ 60000000 + 50 + 300 + 2 = 60000352 \] Ahora, para que se cumpla la igualdad con \(60050302\), necesitamos que el término \(5 \cdot 10^{\square}\) complete la diferencia: \[ 60050302 - 60000352 = 49950 \] Dividiendo 49950 entre 5, encontramos que: \[ \frac{49950}{5} = 9990 \] Esto nos indica que \(10^{\square} = 9990\). Entonces la posición de la cifra \(9\) nos sugiere que \(\square = 4\) (ya que \(10^{4} = 10000\)), precisamente \(5 \cdot 10^{4}\) es el término correcto que completa la igualdad: Finalmente, \(6 \cdot 10^{7} + 5 \cdot 10^{4} + 3 \cdot 10^{2} + 2 \cdot 10^{0} = 60050302\), donde \(\square\) se convierte en \(4\).

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