To simplify these expressions and convert the results into scientific notation, let us proceed step-by-step for each expression.
### Part (a)
Expression: [tex]\(\frac{0.0000625}{0.0005}\)[/tex]
1. To simplify the fraction, perform the division:
[tex]\[
\frac{0.0000625}{0.0005} = 0.125
\][/tex]
2. Convert [tex]\(0.125\)[/tex] into scientific notation:
[tex]\[
0.125 = 1.25 \times 10^{-1}
\][/tex]
Thus, the simplified expression in scientific notation is:
[tex]\[
\frac{0.0000625}{0.0005} = 1.25 \times 10^{-1}
\][/tex]
### Part (b)
Expression: [tex]\(\frac{0.0000000004096}{0.00064}\)[/tex]
1. To simplify the fraction, perform the division:
[tex]\[
\frac{0.0000000004096}{0.00064} = 0.00000064
\][/tex]
2. Convert [tex]\(0.00000064\)[/tex] into scientific notation:
[tex]\[
0.00000064 = 6.40 \times 10^{-7}
\][/tex]
Thus, the simplified expression in scientific notation is:
[tex]\[
\frac{0.0000000004096}{0.00064} = 6.40 \times 10^{-7}
\][/tex]
### Part (c)
Expression: [tex]\(\frac{0.00016807}{0.000343}\)[/tex]
1. To simplify the fraction, perform the division:
[tex]\[
\frac{0.00016807}{0.000343} = 0.49
\][/tex]
2. Convert [tex]\(0.49\)[/tex] into scientific notation:
[tex]\[
0.49 = 4.90 \times 10^{-1}
\][/tex]
Thus, the simplified expression in scientific notation is:
[tex]\[
\frac{0.00016807}{0.000343} = 4.90 \times 10^{-1}
\][/tex]
### Part (d)
Expression: [tex]\(\frac{0.0000006561}{0.00081}\)[/tex]
1. To simplify the fraction, perform the division:
[tex]\[
\frac{0.0000006561}{0.00081} = 0.00000081
\][/tex]
2. Convert [tex]\(0.00000081\)[/tex] into scientific notation:
[tex]\[
0.00000081 = 8.10 \times 10^{-4}
\][/tex]
Thus, the simplified expression in scientific notation is:
[tex]\[
\frac{0.0000006561}{0.00081} = 8.10 \times 10^{-4}
\][/tex]
### Summary of all results:
a. [tex]\(\frac{0.0000625}{0.0005} = 1.25 \times 10^{-1}\)[/tex]
b. [tex]\(\frac{0.0000000004096}{0.00064} = 6.40 \times 10^{-7}\)[/tex]
c. [tex]\(\frac{0.00016807}{0.000343} = 4.90 \times 10^{-1}\)[/tex]
d. [tex]\(\frac{0.0000006561}{0.00081} = 8.10 \times 10^{-4}\)[/tex]
