Solve 200100*1010^3/100left(100+1010^3right)+100*1010^3

$$200 \frac{ 100 \cdot 10 { 10 }^{ 3 } }{ 100 \left( 100+10 { 10 }^{ 3 } \right) +100 \cdot 10 { 10 }^{ 3 } }$$

Evaluate

$$\frac{20000}{201}\approx 99.502487562$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$200\times \frac{100\times 10^{4}}{100\left(100+10\times 10^{3}\right)+100\times 10\times 10^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$200\times \frac{100\times 10^{4}}{100\left(100+10^{4}\right)+100\times 10\times 10^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$200\times \frac{100\times 10^{4}}{100\left(100+10^{4}\right)+100\times 10^{4}}$$

Calculate 10 to the power of 4 and get 10000.

$$200\times \frac{100\times 10000}{100\left(100+10^{4}\right)+100\times 10^{4}}$$

Multiply 100 and 10000 to get 1000000.

$$200\times \frac{1000000}{100\left(100+10^{4}\right)+100\times 10^{4}}$$

Calculate 10 to the power of 4 and get 10000.

$$200\times \frac{1000000}{100\left(100+10000\right)+100\times 10^{4}}$$

Add 100 and 10000 to get 10100.

$$200\times \frac{1000000}{100\times 10100+100\times 10^{4}}$$

Multiply 100 and 10100 to get 1010000.

$$200\times \frac{1000000}{1010000+100\times 10^{4}}$$

Calculate 10 to the power of 4 and get 10000.

$$200\times \frac{1000000}{1010000+100\times 10000}$$

Multiply 100 and 10000 to get 1000000.

$$200\times \frac{1000000}{1010000+1000000}$$

Add 1010000 and 1000000 to get 2010000.

$$200\times \frac{1000000}{2010000}$$

Reduce the fraction \frac{1000000}{2010000} to lowest terms by extracting and canceling out 10000.

$$200\times \frac{100}{201}$$

Express 200\times \frac{100}{201} as a single fraction.

$$\frac{200\times 100}{201}$$

Multiply 200 and 100 to get 20000.

$$\frac{20000}{201}$$

Factor

$$\frac{2 ^ {5} \cdot 5 ^ {4}}{3 \cdot 67} = 99\frac{101}{201} = 99.50248756218906$$