Solve (1/238*6.022*10^23)*200

$$( \frac{ 1 }{ 238 } \times 6.022 \times { 10 }^{ 23 } ) \times 200$$

Evaluate

$$\frac{60220000000000000000000000}{119}\approx 5.060504202 \cdot 10^{23}$$

Solution Steps

Convert decimal number 6.022 to fraction \frac{6022}{1000}. Reduce the fraction \frac{6022}{1000} to lowest terms by extracting and canceling out 2.

$$\frac{1}{238}\times \frac{3011}{500}\times 10^{23}\times 200$$

Multiply \frac{1}{238} times \frac{3011}{500} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3011}{238\times 500}\times 10^{23}\times 200$$

Do the multiplications in the fraction \frac{1\times 3011}{238\times 500}.

$$\frac{3011}{119000}\times 10^{23}\times 200$$

Calculate 10 to the power of 23 and get 100000000000000000000000.

$$\frac{3011}{119000}\times 100000000000000000000000\times 200$$

Express \frac{3011}{119000}\times 100000000000000000000000 as a single fraction.

$$\frac{3011\times 100000000000000000000000}{119000}\times 200$$

Multiply 3011 and 100000000000000000000000 to get 301100000000000000000000000.

$$\frac{301100000000000000000000000}{119000}\times 200$$

Reduce the fraction \frac{301100000000000000000000000}{119000} to lowest terms by extracting and canceling out 1000.

$$\frac{301100000000000000000000}{119}\times 200$$

Express \frac{301100000000000000000000}{119}\times 200 as a single fraction.

$$\frac{301100000000000000000000\times 200}{119}$$

Multiply 301100000000000000000000 and 200 to get 60220000000000000000000000.

$$\frac{60220000000000000000000000}{119}$$

Factor

$$\frac{3011 \cdot 2 ^ {23} \cdot 5 ^ {22}}{7 \cdot 17} = 5.060504201680672 \times 10^{23}\frac{100}{119} = 5.060504201680672 \times 10^{23}$$