Solve 0.16/12*6.022*10^23

$$\frac { 0.16 } { 12 } \times 6.022 \times 10 ^ { 23 }$$

Evaluate

$$\frac{24088000000000000000000}{3}\approx 8.029333333 \cdot 10^{21}$$

Solution Steps

Expand \frac{0.16}{12} by multiplying both numerator and the denominator by 100.

$$\frac{16}{1200}\times 6.022\times 10^{23}$$

Reduce the fraction \frac{16}{1200} to lowest terms by extracting and canceling out 16.

$$\frac{1}{75}\times 6.022\times 10^{23}$$

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.

$$\frac{1}{75}\times \frac{3011}{500}\times 10^{23}$$

Multiply \frac{1}{75} times \frac{3011}{500} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3011}{75\times 500}\times 10^{23}$$

Do the multiplications in the fraction \frac{1\times 3011}{75\times 500}.

$$\frac{3011}{37500}\times 10^{23}$$

Calculate 10 to the power of 23 and get 100000000000000000000000.

$$\frac{3011}{37500}\times 100000000000000000000000$$

Express \frac{3011}{37500}\times 100000000000000000000000 as a single fraction.

$$\frac{3011\times 100000000000000000000000}{37500}$$

Multiply 3011 and 100000000000000000000000 to get 301100000000000000000000000.

$$\frac{301100000000000000000000000}{37500}$$

Reduce the fraction \frac{301100000000000000000000000}{37500} to lowest terms by extracting and canceling out 12500.

$$\frac{24088000000000000000000}{3}$$

Factor

$$\frac{3011 \cdot 2 ^ {21} \cdot 5 ^ {18}}{3} = 8.029333333333334 \times 10^{21}$$