Solve 1/2left(0.001/1+0.1/9.8right)

$$\frac{ 1 }{ 2 } \left( \frac{ 0.001 }{ 1 } + \frac{ 0.1 }{ 9.8 } \right)$$

Evaluate

$$\frac{549}{98000}\approx 0.005602041$$

Solution Steps

Anything divided by one gives itself.

$$\frac{1}{2}\left(0.001+\frac{0.1}{9.8}\right)$$

Expand \frac{0.1}{9.8} by multiplying both numerator and the denominator by 10.

$$\frac{1}{2}\left(0.001+\frac{1}{98}\right)$$

Convert decimal number 0.001 to fraction \frac{1}{1000}.

$$\frac{1}{2}\left(\frac{1}{1000}+\frac{1}{98}\right)$$

Least common multiple of 1000 and 98 is 49000. Convert \frac{1}{1000} and \frac{1}{98} to fractions with denominator 49000.

$$\frac{1}{2}\left(\frac{49}{49000}+\frac{500}{49000}\right)$$

Since \frac{49}{49000} and \frac{500}{49000} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}\times \frac{49+500}{49000}$$

Add 49 and 500 to get 549.

$$\frac{1}{2}\times \frac{549}{49000}$$

Multiply \frac{1}{2} times \frac{549}{49000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 549}{2\times 49000}$$

Do the multiplications in the fraction \frac{1\times 549}{2\times 49000}.

$$\frac{549}{98000}$$

Factor

$$\frac{61 \cdot 3 ^ {2}}{2 ^ {4} \cdot 5 ^ {3} \cdot 7 ^ {2}} = 0.005602040816326531$$