The US 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. Choose an answer from below:
$2.9219 × 10¹¹
$2.9219 × 10¹³
$1.0183 × 10²⁴
$3.0015 × 10¹³
To find the increase in the debt over the 50-year period, we need to subtract the debt in 1971 from the debt in 2021.
2021 debt - 1971 debt = ($2.9617 × 10¹³) - ($3.98 × 10¹¹) = $2.9617 × 10¹³ - $3.98 × 10¹¹
To subtract these values, we need to have the same exponent for the powers of 10. To do this, we can convert $2.9617 × 10¹³ to scientific notation with the same exponent as $3.98 × 10¹¹, which is $0.29817 × 10¹⁴.
Now we can subtract:
$0.29817 × 10¹⁴ - $3.98 × 10¹¹ = $0.29817 × 10¹⁴ - $0.398 × 10¹⁴ = $0.29817 × 10¹⁴ - $0.39817 × 10¹⁴ = $0.1 × 10¹⁴
Therefore, the increase in the debt over the 50-year period is $0.1 × 10¹⁴, which can be written in scientific notation as $1.0 × 10¹³.
So the answer is $1.0 × 10¹³, which is equivalent to $1.0183 × 10¹³ in scientific notation.
To calculate the increase in US national debt over a 50-year period, we need to subtract the initial debt from the final debt.
The national debt in 1971 was $3.98 × 10¹¹, and in 2021 it was $2.9617 × 10¹³.
Therefore, to find the increase, we subtract the initial debt from the final debt:
($2.9617 × 10¹³) - ($3.98 × 10¹¹)
To subtract these numbers, we need to express them in the same power of 10. Let's convert them both to scientific notation:
$2.9617 × 10¹³ = $0.29617 × 10¹⁴
$3.98 × 10¹¹ = $0.398 × 10¹²
Now, subtracting these values gives:
($0.29617 × 10¹⁴) - ($0.398 × 10¹²)
To subtract these numbers, we need to align the exponents:
($0.29617 × 10¹⁴) - ($0.00398 × 10¹⁴)
Now, subtracting the values gives:
$0.29219 × 10¹⁴
Converting this back to standard notation gives:
$2.9219 × 10¹³
Therefore, the increase in the national debt over 50 years was $2.9219 × 10¹³. Thus, the correct answer is:
$2.9219 × 10¹³
To find the increase in the US national debt over a 50-year period, subtract the debt in 1971 from the debt in 2021.
Debt increase = $2.9617 × 10¹³ - $3.98 × 10¹¹
To subtract these values, we need to make sure they have the same exponent. We can do this by multiplying the debt in 1971 by 100:
Debt increase = $2.9617 × 10¹³ - $3.98 × 10¹¹ * 100
Debt increase = $2.9617 × 10¹³ - $3.98 × 10¹³
Debt increase = ($2.9617 - $3.98) × 10¹³
Debt increase = $(-1.0183) × 10¹³
Therefore, the debt increased by $1.0183 × 10¹³ in the 50-year period.
The correct answer is $1.0183 × 10¹³.