Question

calculate 5.3 x 10^-3 - 6.7 x 10 ^ -6. Express the answer in scientific notation rounding to 2 decimal places.

Answer 1

To perform the calculation \( 5.3 \times 10^{-3} - 6.7 \times 10^{-6} \), we need to express both numbers with the same exponent.

1. Convert \( 5.3 \times 10^{-3} \) to the same exponent as \( 6.7 \times 10^{-6} \):
\[
5.3 \times 10^{-3} = 5.3 \times 10^{-3} \times \frac{1000}{1000} = 5.3 \times 10^{-3} = 5.3 \times 10^{-3} = 5300 \times 10^{-6}
\]

2. Now we subtract:
\[
5300 \times 10^{-6} - 6.7 \times 10^{-6} = (5300 - 6.7) \times 10^{-6} = 5293.3 \times 10^{-6}
\]

3. Now, convert \( 5293.3 \times 10^{-6} \) into scientific notation:
\[
5293.3 = 5.2933 \times 10^3
\]
Therefore:
\[
5293.3 \times 10^{-6} = 5.2933 \times 10^{-3}
\]

4. Finally, round to 2 decimal places:
\[
5.2933 \text{ rounds to } 5.29
\]

Thus, the final answer in scientific notation is:
\[
\boxed{5.29 \times 10^{-3}}
\]