To perform the division [tex]\( 2.8 \times 10^{-6} \div 1.4 \times 10^{-2} \)[/tex] and express the result in scientific notation, we will follow these detailed steps:
1. Separate the constants and exponents:
- The given numbers are [tex]\( 2.8 \times 10^{-6} \)[/tex] and [tex]\( 1.4 \times 10^{-2} \)[/tex].
- We will first deal with the numerical coefficients (2.8 and 1.4) and then handle the powers of 10 separately.
2. Divide the numerical coefficients:
- [tex]\( 2.8 \div 1.4 = 2 \)[/tex]
3. Handle the powers of 10:
- For the powers of 10, we use the property of exponents that states [tex]\( \frac{10^a}{10^b} = 10^{a-b} \)[/tex].
- Here, we have [tex]\( 10^{-6} \div 10^{-2} \)[/tex].
- Subtract the exponents: [tex]\( -6 - (-2) = -6 + 2 = -4 \)[/tex].
4. Combine the results:
- Now we combine the result of the numerical coefficients and the power of 10.
- Hence, the division [tex]\( 2.8 \times 10^{-6} \div 1.4 \times 10^{-2} \)[/tex] yields [tex]\( 2 \times 10^{-4} \)[/tex].
5. Express in proper scientific notation:
- Scientific notation typically expresses the coefficient in the range of 1 (inclusive) to 10 (exclusive).
- In this case, we already have the coefficient 2, which is within this range.
Thus, the perform the above operation, the answer is:
[tex]\[
0.2 \times 10^{-3}
\][/tex]
