Solve (99.98%*1)+(2*0.2%)+(3*0.0%)

$$(99.98 \% \times 1)+(2 \times 0.2 \% )+(3 \times 0.0 \% )$$

Evaluate

$$1.0038$$

Solution Steps

Expand \frac{99.98}{100} by multiplying both numerator and the denominator by 100.

$$\frac{9998}{10000}\times 1+2\times \frac{0.2}{100}+3\times \frac{0}{100}$$

Reduce the fraction \frac{9998}{10000} to lowest terms by extracting and canceling out 2.

$$\frac{4999}{5000}\times 1+2\times \frac{0.2}{100}+3\times \frac{0}{100}$$

Multiply \frac{4999}{5000} and 1 to get \frac{4999}{5000}.

$$\frac{4999}{5000}+2\times \frac{0.2}{100}+3\times \frac{0}{100}$$

Expand \frac{0.2}{100} by multiplying both numerator and the denominator by 10.

$$\frac{4999}{5000}+2\times \frac{2}{1000}+3\times \frac{0}{100}$$

Reduce the fraction \frac{2}{1000} to lowest terms by extracting and canceling out 2.

$$\frac{4999}{5000}+2\times \frac{1}{500}+3\times \frac{0}{100}$$

Multiply 2 and \frac{1}{500} to get \frac{2}{500}.

$$\frac{4999}{5000}+\frac{2}{500}+3\times \frac{0}{100}$$

Reduce the fraction \frac{2}{500} to lowest terms by extracting and canceling out 2.

$$\frac{4999}{5000}+\frac{1}{250}+3\times \frac{0}{100}$$

Least common multiple of 5000 and 250 is 5000. Convert \frac{4999}{5000} and \frac{1}{250} to fractions with denominator 5000.

$$\frac{4999}{5000}+\frac{20}{5000}+3\times \frac{0}{100}$$

Since \frac{4999}{5000} and \frac{20}{5000} have the same denominator, add them by adding their numerators.

$$\frac{4999+20}{5000}+3\times \frac{0}{100}$$

Add 4999 and 20 to get 5019.

$$\frac{5019}{5000}+3\times \frac{0}{100}$$

Zero divided by any non-zero number gives zero.

$$\frac{5019}{5000}+3\times 0$$

Multiply 3 and 0 to get 0.

$$\frac{5019}{5000}+0$$

Add \frac{5019}{5000} and 0 to get \frac{5019}{5000}.

$$\frac{5019}{5000}$$

Factor

$$\frac{3 \cdot 7 \cdot 239}{2 ^ {3} \cdot 5 ^ {4}} = 1\frac{19}{5000} = 1.0038$$