To find how much the U.S. national debt increased from 1971 to 2021, we will subtract the debt in 1971 from the debt in 2021.
Given:
- National debt in 2021 = \(2.9617 \times 10^{13}\)
- National debt in 1971 = \(3.98 \times 10^{11}\)
Step 1: Align the numbers in standard form
- Convert both numbers to the same exponent format:
\(3.98 \times 10^{11}\) can be rewritten as: \[ 3.98 \times 10^{11} = 0.0398 \times 10^{13} \]
Step 2: Perform the subtraction
Now we can subtract:
\[ 2.9617 \times 10^{13} - 0.0398 \times 10^{13} = (2.9617 - 0.0398) \times 10^{13} \]
Calculating the subtraction:
\[ 2.9617 - 0.0398 = 2.9219 \]
Step 3: Write the final result in scientific notation
Thus, the increase in the national debt is:
\[ 2.9219 \times 10^{13} \]
Final Answer
The U.S. national debt increased by approximately \(2.9219 \times 10^{13}\) dollars over the 50-year period from 1971 to 2021.