Question

Each year, the United States' federal costs exceed the anticipated national budget. In fact The last time that the United States government was able to end a fiscal year without accruing more debt was in 1960. This means that due to excessive spending and compounding interest accrued, the United States' national debt has escalated astronomically over the past several decades. The table shown below lists the recorded US national debt amounts, written in standard form, for each decade, from 1960 to the year 2010.

Year US Nation Debt (in US dollars)
1960 $286,330,760,848.37
1970 $370,918,706,949.93
1980 $907,701,000,000.00
1990 $3,233,313,451,777.25
2000 $5,674,178,209,886.86
2010 $13,561,623,030,891.79

For each decade, convert the US national debt amount to a number in scientific notation, rounded to the nearest hundred millions dollars. Enter in numerical answers only.

Answer 1

Explanation :

Scientific notation : It is the representation of expressing the numbers that are too big or too small and are represented in the decimal form with one digit before the decimal point times 10 raise to the power.

For example :

5000 is written as
`5.0* 10^3`

889.9 is written as
`8.899* 10^(-2)`

In this examples, 5000 and 889.9 are written in the standard notation and
`5.0* 10^3` and
`8.899* 10^(-2)` are written in the scientific notation.

If the decimal is shifting to right side, the power of 10 is negative and if the decimal is shifting to left side, the power of 10 is positive.

As we are given the US national debt amount to a number.

Now converting this into scientific notation and rounded to the nearest hundred millions dollars, we get:

Hundred million dollars =
`10^8\$`

(1) US Nation Debt (in US dollars) : $286,330,760,848.37

Scientific Notation :
`2863* 10^8\$=2.863* 10^3* 10^8\$=2.86* 10^(11)\$`

(2) US Nation Debt (in US dollars) : $370,918,706,949.93

Scientific Notation :
`3709* 10^8\$=3.709* 10^3* 10^8\$=3.709* 10^(11)\$`

(3) US Nation Debt (in US dollars) : $907,701,000,000.00

Scientific Notation :
`9077* 10^8\$=9.077* 10^3* 10^8\$=9.077* 10^(11)\$`

(4) US Nation Debt (in US dollars) : $3,233,313,451,777.25

Scientific Notation :
`32333* 10^8\$=3.2333* 10^4* 10^8\$=3.2333* 10^(12)\$`

(5) US Nation Debt (in US dollars) : $5,674,178,209,886.86

Scientific Notation :
`56741* 10^8\$=5.6741* 10^4* 10^8\$=5.6741* 10^(12)\$`

(6) US Nation Debt (in US dollars) : $13,561,623,030,891.79

Scientific Notation :
`135616* 10^8\$=1.35616* 10^5* 10^8\$=1.35616* 10^(13)\$`

Answer 2

Given the US National Debt,

1960 $286,330,760,848.37

1970 $370,918,706,949.93

1980 $907,701,000,000.00

1990 $3,233,313,451,777.25

2000 $5,674,178,209,886.86

2010 $13,561,623,030,891.79

Then, rounding off these numbers to nearest hundred million,

1960 $286,000,000,000.00

1970 $370,900,000,000.00

1980 $907,700,000,000.00

1990 $3,233,300,000,000.00

2000 $5,674,200,000,000.00

2010 $13,561,600,000,000.00

While representing a number in scientific notation, it is written as a number between 1 and 10 and then multiplied by a power of 10.

The debt amount becomes,

1960 $2.86×10¹¹

1970 $3.709×10¹¹

1980 $9.077×10¹¹

1990 $3.2333×10¹²

2000 $5.6742×10¹²

2010 $1.35616×10¹³