Let's solve the given mathematical expression step by step.
The expression we need to evaluate is:
[tex]\[ 2.1 \times 10^3 \times 1.2 \times 10^2 + 1.5 \times 10^2 \][/tex]
1. Identify the components you need to work with:
- [tex]\( a = 2.1 \times 10^3 \)[/tex]
- [tex]\( b = 1.2 \times 10^2 \)[/tex]
- [tex]\( c = 1.5 \times 10^2 \)[/tex]
2. First, let's handle the multiplication part:
[tex]\[ 2.1 \times 10^3 \times 1.2 \times 10^2 \][/tex]
Combine the coefficients (numerical parts) and the powers of 10 separately:
[tex]\[ (2.1 \times 1.2) \times (10^3 \times 10^2) \][/tex]
Calculate the numerical part:
[tex]\[ 2.1 \times 1.2 = 2.52 \][/tex]
Calculate the powers of 10:
[tex]\[ 10^3 \times 10^2 = 10^{3+2} = 10^5 \][/tex]
Therefore, the multiplication simplifies to:
[tex]\[ 2.52 \times 10^5 \][/tex]
3. Convert [tex]\( 2.52 \times 10^5 \)[/tex] to a standard decimal number:
[tex]\[ 2.52 \times 10^5 = 252000.0 \][/tex]
4. Next, sum this result with [tex]\( 1.5 \times 10^2 \)[/tex]:
First, convert [tex]\( 1.5 \times 10^2 \)[/tex] to a standard decimal number:
[tex]\[ 1.5 \times 10^2 = 150.0 \][/tex]
Now add [tex]\( 252000.0 \)[/tex] and [tex]\( 150.0 \)[/tex]:
[tex]\[ 252000.0 + 150.0 = 252150.0 \][/tex]
So, the final result of evaluating the expression [tex]\( 2.1 \times 10^3 \times 1.2 \times 10^2 + 1.5 \times 10^2 \)[/tex] is:
[tex]\[ \boxed{252150.0} \][/tex]
