Resolver {l}{400*20000}{37*2000}{(4*10^{-3})(2*10^{5})}{(3*10^-1)(6*10^-8)}{(6.7*10^3)(4.0*10^5)}

$$\left. \begin{array} { l } { 400 \times 20000 } \\ { 37 \times 2000 } \\ { ( 4 \times 10 ^ { - 3 } ) ( 2 \times 10 ^ { 5 } ) } \\ { ( 3 \times 10 ^ { - 1 } ) ( 6 \times 10 ^ { - 8 } ) } \\ { ( 6.7 \times 10 ^ { 3 } ) ( 4.0 \times 10 ^ { 5 } ) } \end{array} \right.$$

Ordenar

$$0.000000018,800,74000,8000000,2680000000$$

Pasos da solución

Para multiplicar potencias da mesma base, suma os seus expoñentes. Suma -3 e 5 para obter 2.

$$sort(400\times 20000,37\times 2000,4\times 10^{2}\times 2,3\times 10^{-1}\times 6\times 10^{-8},6.7\times 10^{3}\times 4\times 10^{5})$$

Para multiplicar potencias da mesma base, suma os seus expoñentes. Suma -1 e -8 para obter -9.

$$sort(400\times 20000,37\times 2000,4\times 10^{2}\times 2,3\times 10^{-9}\times 6,6.7\times 10^{3}\times 4\times 10^{5})$$

Para multiplicar potencias da mesma base, suma os seus expoñentes. Suma 3 e 5 para obter 8.

$$sort(400\times 20000,37\times 2000,4\times 10^{2}\times 2,3\times 10^{-9}\times 6,6.7\times 10^{8}\times 4)$$

Multiplica 400 e 20000 para obter 8000000.

$$sort(8000000,37\times 2000,4\times 10^{2}\times 2,3\times 10^{-9}\times 6,6.7\times 10^{8}\times 4)$$

Multiplica 37 e 2000 para obter 74000.

$$sort(8000000,74000,4\times 10^{2}\times 2,3\times 10^{-9}\times 6,6.7\times 10^{8}\times 4)$$

Calcula 10 á potencia de 2 e obtén 100.

$$sort(8000000,74000,4\times 100\times 2,3\times 10^{-9}\times 6,6.7\times 10^{8}\times 4)$$

Multiplica 4 e 100 para obter 400.

$$sort(8000000,74000,400\times 2,3\times 10^{-9}\times 6,6.7\times 10^{8}\times 4)$$

Multiplica 400 e 2 para obter 800.

$$sort(8000000,74000,800,3\times 10^{-9}\times 6,6.7\times 10^{8}\times 4)$$

Calcula 10 á potencia de -9 e obtén \frac{1}{1000000000}.

$$sort(8000000,74000,800,3\times \frac{1}{1000000000}\times 6,6.7\times 10^{8}\times 4)$$

Multiplica 3 e \frac{1}{1000000000} para obter \frac{3}{1000000000}.

$$sort(8000000,74000,800,\frac{3}{1000000000}\times 6,6.7\times 10^{8}\times 4)$$

Multiplica \frac{3}{1000000000} e 6 para obter \frac{9}{500000000}.

$$sort(8000000,74000,800,\frac{9}{500000000},6.7\times 10^{8}\times 4)$$

Calcula 10 á potencia de 8 e obtén 100000000.

$$sort(8000000,74000,800,\frac{9}{500000000},6.7\times 100000000\times 4)$$

Multiplica 6.7 e 100000000 para obter 670000000.

$$sort(8000000,74000,800,\frac{9}{500000000},670000000\times 4)$$

Multiplica 670000000 e 4 para obter 2680000000.

$$sort(8000000,74000,800,\frac{9}{500000000},2680000000)$$

Converte números decimais na lista 8000000,74000,800,\frac{9}{500000000},2680000000 a fraccións.

$$8000000,74000,800,\frac{9}{500000000},2680000000$$

Para ordenar a lista, empeza por un único elemento 8000000.

$$8000000$$

Insire 74000 na localización axeitada na nova lista.

$$74000,8000000$$

Insire 800 na localización axeitada na nova lista.

$$800,74000,8000000$$

Insire \frac{9}{500000000} na localización axeitada na nova lista.

$$\frac{9}{500000000},800,74000,8000000$$

Insire 2680000000 na localización axeitada na nova lista.

$$\frac{9}{500000000},800,74000,8000000,2680000000$$

Calcular

$$8000000,\ 74000,\ 800,\ 0.000000018,\ 2680000000$$