Which expression is equal to 5.1×10−3

Question

?(1 point)
Responses

2.2×10−1+2.9×10−2
2.2 times 10 superscript negative 1 baseline plus 2.9 times 10 negative squared

3.9×10−3+1.2×10−3
3.9 times 10 negative cubed plus 1.2 times 10 negative cubed

2.9×10−3+1.2×10−3
2.9 times 10 negative cubed plus 1.2 times 10 negative cubed

3.5×103+1.6×10−6

Answer 1

To determine which expression is equal to \(5.1 \times 10^{-3}\), let's simplify each option one by one.

1. Option 1: \(2.2 \times 10^{-1} + 2.9 \times 10^{-2}\)
   Convert \(2.2 \times 10^{-1}\) to a smaller power of ten:
   \(2.2 \times 10^{-1} = 2.2 \times 10^{-1} = 22 \times 10^{-2}\)
   Now we can add:
   \(22 \times 10^{-2} + 2.9 \times 10^{-2} = (22 + 2.9) \times 10^{-2} = 24.9 \times 10^{-2} = 2.49 \times 10^{-1}\)
   This does not equal \(5.1 \times 10^{-3}\).

2. Option 2: \(3.9 \times 10^{-3} + 1.2 \times 10^{-3}\)
   Adding these together:
   \(3.9 \times 10^{-3} + 1.2 \times 10^{-3} = (3.9 + 1.2) \times 10^{-3} = 5.1 \times 10^{-3}\)
   This equals \(5.1 \times 10^{-3}\).

3. Option 3: \(2.9 \times 10^{-3} + 1.2 \times 10^{-3}\)
   Adding these together:
   \(2.9 \times 10^{-3} + 1.2 \times 10^{-3} = (2.9 + 1.2) \times 10^{-3} = 4.1 \times 10^{-3}\)
   This does not equal \(5.1 \times 10^{-3}\).

4. Option 4: \(3.5 \times 10^{3} + 1.6 \times 10^{-6}\)
   These terms are vastly different in scale and their sum will not be anywhere near \(5.1 \times 10^{-3}\).

From the above calculations, the only expression that equals \(5.1 \times 10^{-3}\) is Option 2: \(3.9 \times 10^{-3} + 1.2 \times 10^{-3}\).