Sure, let’s solve the problem step by step:
We need to multiply two numbers:
[tex]\[ \left(3 \times 10^{-6}\right) \text{ and } \left(1.2 \times 10^5\right) \][/tex]
1. Step 1: Separate and handle the coefficients:
We have the numbers:
[tex]\[ 3 \][/tex]
and
[tex]\[ 1.2 \][/tex]
Multiplying these two gives:
[tex]\[ 3 \times 1.2 = 3.6 \][/tex]
2. Step 2: Handle the powers of 10:
We have:
[tex]\[ 10^{-6} \][/tex]
and
[tex]\[ 10^5 \][/tex]
When multiplying powers of 10, you add the exponents:
[tex]\[ 10^{-6 + 5} = 10^{-1} \][/tex]
3. Step 3: Combine the coefficient and the power of 10:
Combine the results from the coefficients and the powers of 10:
[tex]\[ 3.6 \times 10^{-1} \][/tex]
4. Step 4: Simplify the expression:
We can rewrite [tex]\( 3.6 \times 10^{-1} \)[/tex] as:
[tex]\[ 3.6 \times 0.1 = 0.36 \][/tex]
Thus, the product of [tex]\( \left(3 \times 10^{-6}\right) \)[/tex] and [tex]\( \left(1.2 \times 10^5\right) \)[/tex] is:
[tex]\[ 0.36 \][/tex]
So, the final answer is:
[tex]\[ 0.36 \][/tex]
