To solve this problem, we start by understanding and using the given details step-by-step:
1. Given Information:
- GDP: \[tex]$4.87 trillion (which is equivalent to \$[/tex]4.87 \times 10^{12}[tex]$).
- Inflation rate: 2.5\% (or 0.025 as a decimal).
- Population: 127,502,000.
2. Calculate the Real GDP:
The formula for calculating the Real GDP is given by:
\[
\text{Real GDP} = \text{GDP} - (\text{GDP} \times \text{Inflation Rate})
\]
Plugging in the given values:
\[
\text{Real GDP} = 4.87 \times 10^{12} - (4.87 \times 10^{12} \times 0.025)
\]
Compute the product of GDP and the inflation rate:
\[
4.87 \times 10^{12} \times 0.025 = 0.12175 \times 10^{12}
\]
Subtract this from the original GDP:
\[
\text{Real GDP} = 4.87 \times 10^{12} - 0.12175 \times 10^{12} = 4.74825 \times 10^{12}
\]
Therefore, the Real GDP is 4.74825 trillion dollars, which written out in full numerical form is:
\[
\text{Real GDP} = 4,748,250,000,000 \, \text{(dollars)}
\]
3. Calculate Per Capita GDP:
The formula for Per Capita GDP is:
\[
\text{Per Capita GDP} = \frac{\text{Real GDP}}{\text{Population}}
\]
Substituting the Real GDP and population:
\[
\text{Per Capita GDP} = \frac{4,748,250,000,000}{127,502,000}
\]
Perform the division:
\[
\text{Per Capita GDP} = 37,240.5902512
\]
Rounding to the nearest cent:
\[
\text{Per Capita GDP} = \$[/tex]37,240.59
\]
Therefore, the Per Capita GDP in Japan, rounded to the nearest cent, is:
[tex]\[
\boxed{\$37,240.59}
\][/tex]
