5×10-¹+2×10-²+1×10-⁴

To calculate the expression \( 5 \times 10^{-1} + 2 \times 10^{-2} + 1 \times 10^{-4} \), we should first convert each term to have the same power of ten for easier addition. 1. Convert \( 5 \times 10^{-1} \) to \( 10^{-2} \): \[ 5 \times 10^{-1} = 5 \times 10^{-1} \times \frac{10}{10} = 50 \times 10^{-2} \] 2. Convert \( 2 \times 10^{-2} \) to \( 10^{-2} \): \[ 2 \times 10^{-2} = 2 \times 10^{-2} \] (It's already in \( 10^{-2} \) form.) 3. Convert \( 1 \times 10^{-4} \) to \( 10^{-2} \): \[ 1 \times 10^{-4} = 1 \times 10^{-4} \times \frac{100}{100} = 0.01 \times 10^{-2} = 0.01 \times 10^{-2} \] Now, we can write the entire expression in terms of \( 10^{-2} \): \[ 50 \times 10^{-2} + 2 \times 10^{-2} + 0.01 \times 10^{-2} \] Now add the coefficients: \[ (50 + 2 + 0.01) \times 10^{-2} = 52.01 \times 10^{-2} \] Finally, express it in a standard scientific notation form: \[ 52.01 \times 10^{-2} = 5.201 \times 10^{-1} \] Thus, the final result is: \[ \boxed{5.201 \times 10^{-1}} \]