To determine which expression is equal to \( 5.1 \times 10^{-3} \), let's evaluate each option by calculating their sums:
Option A: \[ 2.2 \times 10^{-1} + 2.9 \times 10^{-2} = 2.2 \times 10^{-1} + 0.029 \] First, convert \( 2.2 \times 10^{-1} \) to decimal: \[ 2.2 \times 10^{-1} = 0.22 \] Now add: \[ 0.22 + 0.029 = 0.249 \] Convert to scientific notation: \[ 0.249 = 2.49 \times 10^{-1} \quad (\text{not matching } 5.1 \times 10^{-3}) \]
Option B: \[ 2.9 \times 10^{-3} + 1.2 \times 10^{-3} \] Combine the coefficients: \[ 2.9 + 1.2 = 4.1 \] Thus, \[ 4.1 \times 10^{-3} \quad (\text{not matching } 5.1 \times 10^{-3}) \]
Option C: \[ 3.5 \times 10^{3} + 1.6 \times 10^{-6} \] The first term \( 3.5 \times 10^{3} \) is much larger than \( 5.1 \times 10^{-3} \) and will dominate. Calculating yields: \[ 3.5 \times 10^{3} \quad (\text{not matching } 5.1 \times 10^{-3}) \]
Option D: \[ 3.9 \times 10^{-3} + 1.2 \times 10^{-3} \] Combine the coefficients: \[ 3.9 + 1.2 = 5.1 \] Thus, \[ 5.1 \times 10^{-3} \quad (\text{matching } 5.1 \times 10^{-3}) \]
The expression that is equal to \( 5.1 \times 10^{-3} \) is Option D: \( 3.9 \times 10^{-3} + 1.2 \times 10^{-3} \).