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.
A. $3.0015 × 10¹³
B. $1.0183 × 10²⁴
C. $2.9219 × 10¹¹
D. $2.9219 × 10¹³
To find the increase in the national debt over the 50-year period, we simply subtract the initial debt from the final debt.
Final debt in 2021: $2.9617 × 10¹³
Initial debt in 1971: $3.98 × 10¹¹
Increase in debt = Final debt - Initial debt
Increase in debt = ($2.9617 × 10¹³) - ($3.98 × 10¹¹)
To subtract these values, we need to express them in the same exponent format.
Final debt = $29.617 × 10¹²
Initial debt = $0.398 × 10¹³
Increase in debt = ($29.617 × 10¹²) - ($0.398 × 10¹³)
Now, let's subtract these values:
Increase in debt = $29.617 × 10¹² - $0.398 × 10¹³
Increase in debt = $29.617 × 10¹² - $0.0398 × 10¹⁴ (we move the decimal point one place to the right because the exponent increased by one)
Now, let's subtract:
Increase in debt = $29.5772 × 10¹² (we express it back in scientific notation)
Therefore, the increase in the debt over the 50-year period is $2.95772 × 10¹¹, which is approximately $2.9579 × 10¹³.
So, the correct answer is D. $2.9579 × 10¹³.
To find how much the debt increased in the 50-year period, we need to subtract the debt in 1971 from the debt in 2021.
Debt increase = Debt in 2021 - Debt in 1971
Debt in 2021 = $2.9617 × 10¹³
Debt in 1971 = $3.98 × 10¹¹
Debt increase = ($2.9617 × 10¹³) - ($3.98 × 10¹¹)
To subtract these numbers, we need to have them in the same order of magnitude. We can convert $3.98 × 10¹¹ to $3.98 × 10¹³ by multiplying it by 100.
Debt increase = ($2.9617 × 10¹³) - ($3.98 × 10¹¹ × 100)
= $2.9617 × 10¹³ - $3.98 × 10¹³
= $2.9617 × 10¹³ - $3.98 × 10¹³
= ($2.9617 - $3.98) × 10¹³
= $(-1.0183) × 10¹³
Therefore, the debt increased by $1.0183 × 10¹³ in the 50-year period.
The correct answer is B. $1.0183 × 10¹³.
To find the increase in the U.S. national debt over the 50-year period, we need to subtract the initial debt in 1971 from the debt in 2021.
Let's first convert the given values to standard form:
Debt in 2021 = $2.9617 × 10¹³
Debt in 1971 = $3.98 × 10¹¹
Now, subtract the debt in 1971 from the debt in 2021:
($2.9617 × 10¹³) - ($3.98 × 10¹¹)
To subtract these numbers, we need to align the exponents. So, we should convert $3.98 × 10¹¹ to scientific notation with an exponent of 13:
$3.98 × 10¹¹ = $0.0398 × 10¹³
Now we can subtract the numbers:
($2.9617 × 10¹³) - ($0.0398 × 10¹³)
The exponents are the same, so we can subtract the coefficients:
2.9617 - 0.0398 = 2.9219
The result is 2.9219 × 10¹³.
Therefore, the debt increased by $2.9219 × 10¹³ in the 50-year period.
So the correct answer is option D. $2.9219 × 10¹³.