To solve this problem, we will carefully follow the information given to us and apply some basic algebraic steps.
1. Identify the relationships given in the problem:
- The mass of object [tex]\( A \)[/tex] is [tex]\( 483 \% \)[/tex] of the mass of object [tex]\( B \)[/tex]. This can be expressed as:
[tex]\[
\text{mass of } A = 483 \% \times \text{mass of } B = 4.83 \times \text{mass of } B
\][/tex]
- The mass of object [tex]\( A \)[/tex] is [tex]\( 0.069 \% \)[/tex] of the mass of object [tex]\( C \)[/tex]. This can be expressed as:
[tex]\[
\text{mass of } A = 0.069 \% \times \text{mass of } C = 0.00069 \times \text{mass of } C
\][/tex]
2. Set up equations based on the above relationships:
From the first relationship:
[tex]\[
m_A = 4.83 \times m_B
\][/tex]
where [tex]\( m_A \)[/tex] is the mass of object [tex]\( A \)[/tex] and [tex]\( m_B \)[/tex] is the mass of object [tex]\( B \)[/tex].
From the second relationship:
[tex]\[
m_A = 0.00069 \times m_C
\][/tex]
where [tex]\( m_C \)[/tex] is the mass of object [tex]\( C \)[/tex].
3. Combine the two equations to eliminate [tex]\( m_A \)[/tex] and solve for [tex]\( m_C \)[/tex]:
Since both equations equal [tex]\( m_A \)[/tex], we can set them equal to each other:
[tex]\[
4.83 \times m_B = 0.00069 \times m_C
\][/tex]
4. Solve for [tex]\( m_C \)[/tex] in terms of [tex]\( m_B \)[/tex]:
Rearrange the equation to solve for [tex]\( m_C \)[/tex]:
[tex]\[
m_C = \frac{4.83 \times m_B}{0.00069}
\][/tex]
Through direct division:
[tex]\[
m_C = 6999.999 \times m_B
\][/tex]
5. Determine [tex]\( p \% \)[/tex] which represents the mass of [tex]\( C \)[/tex] in terms of the mass of [tex]\( B \)[/tex]:
The mass of object [tex]\( C \)[/tex] as a percentage of the mass of object [tex]\( B \)[/tex] is:
[tex]\[
p = \left(\frac{m_C}{m_B}\right) \times 100
\][/tex]
Substituting [tex]\( m_C = 6999.999 \times m_B \)[/tex]:
[tex]\[
p = \left(\frac{6999.999 \times m_B}{m_B}\right) \times 100 = 699999.999 \%
\][/tex]
6. Finally, the value of [tex]\(\frac{p}{1.000}\)[/tex]:
Since [tex]\( \frac{p}{1.000} = \frac{699999.999}{1.000} \)[/tex]:
Thus:
[tex]\[
\frac{p}{1.000} = 699999.999
\][/tex]
So, the value of [tex]\( \frac{p}{1.000} \)[/tex] is [tex]\( 699999.999 \)[/tex].
