Let's analyze the changes in the percentage of world manufacturing for each country from 1870 to 1913 step by step.
1. United States:
- In 1870: 23%
- In 1913: 36%
- Percentage increase: [tex]\( 36\% - 23\% = 13\% \)[/tex]
2. Germany:
- In 1870: 13%
- In 1913: 16%
- Percentage increase: [tex]\( 16\% - 13\% = 3\% \)[/tex]
3. Great Britain:
- In 1870: 32%
- In 1913: 14%
- Percentage decrease: [tex]\( 14\% - 32\% = -18\% \)[/tex]
4. France:
- In 1870: 10%
- In 1913: 6%
- Percentage decrease: [tex]\( 6\% - 10\% = -4\% \)[/tex]
5. Russia:
- In 1870: 4%
- In 1913: 6%
- Percentage increase: [tex]\( 6\% - 4\% = 2\% \)[/tex]
6. Belgium:
- In 1870: 3%
- In 1913: 2%
- Percentage decrease: [tex]\( 2\% - 3\% = -1\% \)[/tex]
From these calculations, we can see that the United States showed the greatest percentage increase in world manufacturing from 1870 to 1913 with an increase of 13%.
Therefore, the correct answer is: the United States.