Sure, let's solve each of the expressions step-by-step:
### Part i) [tex]\(1.3 \times 10^5 - 4.9 \times 10^4\)[/tex]
1. First, express each term in standard form:
[tex]\[
1.3 \times 10^5 = 130000
\][/tex]
[tex]\[
4.9 \times 10^4 = 49000
\][/tex]
2. Subtract the second term from the first:
[tex]\[
130000 - 49000 = 81000
\][/tex]
So, the result is:
[tex]\[
81000.0
\][/tex]
### Part ii) [tex]\(3.3 \times 10^{-4} - 5.2 \times 10^{-3}\)[/tex]
1. First, express each term in standard form:
[tex]\[
3.3 \times 10^{-4} = 0.00033
\][/tex]
[tex]\[
5.2 \times 10^{-3} = 0.0052
\][/tex]
2. Subtract the second term from the first:
[tex]\[
0.00033 - 0.0052 = -0.00487
\][/tex]
So, the result is:
[tex]\[
-0.00487
\][/tex]
### Part iii) [tex]\(4.8 \times 10^{-5} - 3.5 \times 10^{-6}\)[/tex]
1. First, express each term in standard form:
[tex]\[
4.8 \times 10^{-5} = 0.000048
\][/tex]
[tex]\[
3.5 \times 10^{-6} = 0.0000035
\][/tex]
2. Subtract the second term from the first:
[tex]\[
0.000048 - 0.0000035 = 0.0000445
\][/tex]
Express the result back in scientific notation:
[tex]\[
0.0000445 = 4.45 \times 10^{-5}
\][/tex]
So, the result is:
[tex]\[
4.45 \times 10^{-5}
\][/tex]
### Part iv) [tex]\(5.4 \times 10^{-3} - 8.6 \times 10^{-5}\)[/tex]
1. First, express each term in standard form:
[tex]\[
5.4 \times 10^{-3} = 0.0054
\][/tex]
[tex]\[
8.6 \times 10^{-5} = 0.000086
\][/tex]
2. Subtract the second term from the first:
[tex]\[
0.0054 - 0.000086 = 0.005314
\][/tex]
So, the result is:
[tex]\[
0.005314
\][/tex]
### Summary
- Part i) [tex]\(1.3 \times 10^5 - 4.9 \times 10^4 = 81000.0\)[/tex]
- Part ii) [tex]\(3.3 \times 10^{-4} - 5.2 \times 10^{-3} = -0.00487\)[/tex]
- Part iii) [tex]\(4.8 \times 10^{-5} - 3.5 \times 10^{-6} = 4.45 \times 10^{-5}\)[/tex]
- Part iv) [tex]\(5.4 \times 10^{-3} - 8.6 \times 10^{-5} = 0.005314\)[/tex]
