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

$2.9219×1011
2.9219 dollars times 10 superscript 11 baseline

$2.9219×1013
2.9219 dollars times 10 superscript 13 baseline

$3.0015×1013
3.0015 dollars times 10 superscript 13 baseline

$1.0183×1024

Answer 1

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

The debts in scientific notation are:

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

First, we need to express both numbers using the same exponent. To do this, we'll convert \( 3.98 \times 10^{11} \) to have an exponent of 13:

\[ 3.98 \times 10^{11} = 3.98 \times 10^{11} \times \frac{10^{2}}{10^{2}} = 3.98 \times 10^{13} \div 100 = 0.0398 \times 10^{13} \]

Now both numbers can be expressed in terms of \( 10^{13} \):

• 2021 debt: \( 2.9617 \times 10^{13} \)
• 1971 debt: \( 0.0398 \times 10^{13} \)

Now we can subtract:

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

Therefore, the increase in the national debt over the 50-year period is:

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