Which expression is equal to 5.1×10−3

Question

?(1 point)
Responses

2.2×10−1+2.9×10−2
2 point 2 times 10 inverse plus 2 point 9 times 10 to the negative 2 power - no response given

3.9×10−3+1.2×10−3
3 point 9 times 10 to the negative 3 power plus 1 point 2 times 10 to the negative 3 power - no response given

3.5×103+1.6×10−6
3 point 5 times 10 cubed plus 1 point 6 times 10 to the negative 6 power - no response given

2.9×10−3+1.2×10−3

Answer 1

To determine which expression is equal to \( 5.1 \times 10^{-3} \), we need to evaluate each option individually:

1. \( 2.2 \times 10^{-1} + 2.9 \times 10^{-2} \):

   • Convert \( 2.2 \times 10^{-1} \) to a decimal: \( 2.2 \times 10^{-1} = 0.22 \)
   • Convert \( 2.9 \times 10^{-2} \) to a decimal: \( 2.9 \times 10^{-2} = 0.029 \)
   • Adding these two together: \[ 0.22 + 0.029 = 0.249 = 2.49 \times 10^{-1} \quad \text{(not equal)} \]

2. \( 3.9 \times 10^{-3} + 1.2 \times 10^{-3} \):

   • Convert these to the same exponent: \[ 3.9 \times 10^{-3} + 1.2 \times 10^{-3} = (3.9 + 1.2) \times 10^{-3} = 5.1 \times 10^{-3} \quad \text{(equal)} \]

3. \( 3.5 \times 10^{3} + 1.6 \times 10^{-6} \):

   • Convert \( 3.5 \times 10^{3} \): \( 3.5 \times 10^{3} = 3500 \)
   • Convert \( 1.6 \times 10^{-6} \): \( 1.6 \times 10^{-6} = 0.0000016 \)
   • Adding these together: \[ 3500 + 0.0000016 \quad \text{(not equal)} \]

4. \( 2.9 \times 10^{-3} + 1.2 \times 10^{-3} \):

   • Convert these to the same exponent: \[ 2.9 \times 10^{-3} + 1.2 \times 10^{-3} = (2.9 + 1.2) \times 10^{-3} = 4.1 \times 10^{-3} \quad \text{(not equal)} \]

The only expression equal to \( 5.1 \times 10^{-3} \) is:

\( 3.9 \times 10^{-3} + 1.2 \times 10^{-3} \).