Sure! Let's solve the problem step-by-step.
### Part a)
To solve the expression [tex]\( 2 \times 10^3 + 1.2 \times 10^2 - 1 \)[/tex]:
1. Calculate [tex]\( 2 \times 10^3 \)[/tex]:
[tex]\[
2 \times 10^3 = 2,000
\][/tex]
2. Calculate [tex]\( 1.2 \times 10^2 \)[/tex]:
[tex]\[
1.2 \times 10^2 = 120
\][/tex]
3. Add the results from steps 1 and 2, then subtract 1:
[tex]\[
2,000 + 120 - 1 = 2,119
\][/tex]
So, the result for part (a) is:
[tex]\[
2 \times 10^3 + 1.2 \times 10^2 - 1 = 2,119
\][/tex]
### Part b)
To solve the expression [tex]\( \frac{0.000063 \times 0.000084}{0.00012 \times 0.00003} \)[/tex]:
1. Calculate the numerator [tex]\( 0.000063 \times 0.000084 \)[/tex]:
[tex]\[
0.000063 \times 0.000084 = 5.292 \times 10^{-9}
\][/tex]
2. Calculate the denominator [tex]\( 0.00012 \times 0.00003 \)[/tex]:
[tex]\[
0.00012 \times 0.00003 = 3.6 \times 10^{-9}
\][/tex]
3. Divide the numerator by the denominator:
[tex]\[
\frac{5.292 \times 10^{-9}}{3.6 \times 10^{-9}} = \frac{5.292}{3.6} = 1.47
\][/tex]
So, the result for part (b) is:
[tex]\[
\frac{0.000063 \times 0.000084}{0.00012 \times 0.00003} = 1.47
\][/tex]
### Summary
- [tex]\( 2 \times 10^3 + 1.2 \times 10^2 - 1 = 2,119 \)[/tex]
- [tex]\( \frac{0.000063 \times 0.000084}{0.00012 \times 0.00003} = 1.47 \)[/tex]
These are the answers for parts (a) and (b) respectively.
