The U.S. national debt was $2.9617 \times 10^{13} in 2021 and $3.98 \times 10^{11} in 1971. Find how much the debt increased in the 50-year period. (1 point)

Question

$2.9219 \times 10^{13}

$1.0183 \times 10^{24}

$3.0015 \times 10^{13}

$2.9219 \times 10^{11}

Answer 1

To find the increase in the U.S. national debt from 1971 to 2021, we need to subtract the debt in 1971 from the debt in 2021.

The debt in 2021 is: \[ 2.9617 \times 10^{13} \]

The debt in 1971 is: \[ 3.98 \times 10^{11} \]

To perform the subtraction, it's helpful to express both values with the same exponent. We can rewrite \(3.98 \times 10^{11}\) with a base of \(10^{13}\):

\[ 3.98 \times 10^{11} = 0.0398 \times 10^{13} \]

Now we can subtract the two values:

\[ 2.9617 \times 10^{13} - 0.0398 \times 10^{13} = (2.9617 - 0.0398) \times 10^{13} \]

Calculating \(2.9617 - 0.0398\):

\[ 2.9617 - 0.0398 = 2.9219 \]

Thus, the increase in the national debt is:

\[ 2.9219 \times 10^{13} \]

Now, looking at the options provided, the correct answer is:

\[ \boxed{2.9219 \times 10^{13}} \]