To calculate \( 5.3 \times 10^{-3} - 6.7 \times 10^{-6} \), we need to express both numbers with the same exponent for easier subtraction.
The first number is \( 5.3 \times 10^{-3} \). The second number needs to be expressed with the same exponent. We can convert \( 6.7 \times 10^{-6} \) to a comparable form by expressing it with an exponent of \( -3 \):
\[ 6.7 \times 10^{-6} = 6.7 \times 10^{-6} \times \frac{10^{-3}}{10^{-3}} = 6.7 \times 10^{-3} \times 10^{-3} = 0.0067 \times 10^{-3} \]
Now the expression can be simplified as:
\[ 5.3 \times 10^{-3} - 0.0067 \times 10^{-3} = (5.3 - 0.0067) \times 10^{-3} \] Calculate \( 5.3 - 0.0067 \):
\[ 5.3 - 0.0067 = 5.2933 \]
Thus, we have:
\[ 5.2933 \times 10^{-3} \]
Now we convert \( 5.2933 \times 10^{-3} \) into proper scientific notation. We need to round this to two decimal places:
The first two digits (5.29) remain, and we would ignore further digits beyond that. Therefore, the answer in scientific notation is:
\[ 5.29 \times 10^{-3} \]
Now let's check the options provided:
A. -1.4×10^3
B. 5.29×10^4
C. 1.4×10^3
D. 5.29×10^3
None of the provided options match \[ 5.29 \times 10^{-3} \], which means that it's possible there was a misunderstanding or error in the problem's setup.
However, the calculated value is \(\mathbf{5.29 \times 10^{-3}}.\)