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QuestionFind the scientific notation for 15.55 trillion and \$70,000, then calculate how many citizens can get free college education.

Studdy Solution

STEP 1

Assumptions1. The national debt is 15.55trillion.Fouryearsoftuition,fees,androomandboardatapublicU.S.collegecostapproximately15.55 trillion. Four years of tuition, fees, and room and board at a public U.S. college cost approximately 70,0003. We are asked to express these numbers in scientific notation and then use them to determine how many citizens could receive a free college education for $15.55 trillion

STEP 2

First, we need to express15.55 trillion in scientific notation. In scientific notation, a number is written as a number between1 and10 multiplied by a power of10.15.55 trillion=15.55×101215.55\, trillion =15.55 \times10^{12}

STEP 3

To express this in scientific notation, we need to adjust the number so that it is between1 and10. We do this by moving the decimal point two places to the left.
15.55 trillion=1.555×101415.55\, trillion =1.555 \times10^{14}

STEP 4

Next, we need to express 70,000inscientificnotation.70,000 in scientific notation.$70,000=7×104\$70,000 =7 \times10^{4}$

STEP 5

Now that we have both numbers in scientific notation, we can use them to determine how many citizens could receive a free college education for $15.55 trillion.To do this, we divide the total amount of money (the national debt) by the cost of a college education.
Number of citizens=National debtCost of college educationNumber\, of\, citizens = \frac{National\, debt}{Cost\, of\, college\, education}

STEP 6

Plug in the values for the national debt and the cost of a college education to calculate the number of citizens.
Number of citizens=1.555×1014×104Number\, of\, citizens = \frac{1.555 \times10^{14}}{ \times10^{4}}

STEP 7

implify the division by subtracting the exponent in the denominator from the exponent in the numerator.
Number of citizens=1.555×1014−4/7Number\, of\, citizens =1.555 \times10^{14-4} /7

STEP 8

Calculate the number of citizens.
Number of citizens=1.555×1010/7Number\, of\, citizens =1.555 \times10^{10} /7

STEP 9

Calculate the final answer.
Number of citizens=2.22×9Number\, of\, citizens =2.22 \times^{9}So, approximately2.22 billion citizens could receive a free college education for $15.55 trillion.

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