Question

Which expression is equal to 5.1×10^-3?

A. 2.2×10^-1 + 2.9×10^-2
B. 2.9×10^-3 + 1.2×10^-3
C. 3.5×10^3 + 1.6×10^-6
D. 3.9×10^-3 + 1.2×10^-3

Answer 1

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