Subtract Numbers in Scientific Notation Quick Check

Question

2 of 52 of 5 Items
Question
The U.S. national debt was $2.9617×1013
in 2021 and $3.98×1011
in 1971. Find how much the debt increased in the 50-year period. (1 point)
Responses

$3.0015×1013
3.0015 dollars times 10 superscript 13 baseline

$1.0183×1024
1.0183 dollars times 10 superscript 24 baseline

$2.9219×1013
2.9219 dollars times 10 superscript 13 baseline

$2.9219×1011
2.9219 dollars times 10 superscript 11 baseline
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Answer 1

To find out how much the U.S. national debt increased from 1971 to 2021, you need to subtract the 1971 debt from the 2021 debt.

The debts in scientific notation are:

• 2021: \(2.9617 \times 10^{13}\)
• 1971: \(3.98 \times 10^{11}\)

First, we need to express \(3.98 \times 10^{11}\) in terms of \(10^{13}\) to make the subtraction easier:

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

Now we can perform the subtraction:

\[ 2.9617 \times 10^{13} - 0.0398 \times 10^{13} = (2.9617 - 0.0398) \times 10^{13} \] \[ = 2.9219 \times 10^{13} \]

Thus, the increase in the national debt over the 50-year period is \(2.9219 \times 10^{13}\).

The correct response is:

$2.9219×10^{13}$