Estimate Large and Small Quantities Quick Check

Question

3 of 53 of 5 Items
Question
At the end of fiscal year 2004, the federal debt of Country C is $278,560,125,000. What is the closest estimation of this amount? Express your answer in the form of a single digit times an integer power of 10.(1 point)
Responses

2 × 10^11
2 times 10 superscript 11 baseline

3 × 10^−11
3 times 10 superscript negative 11 baseline

3 × 10^11
3 times 10 superscript 11 baseline

2.79 × 10^11
2.79 times 10 superscript 11 baseline
Skip to navigation

Answer 1

To estimate the federal debt of Country C, which is $278,560,125,000, we can round the number to a single digit followed by the appropriate power of ten.

1. The first step is to notice the leading digits. The number is approximately 280 billion.

2. In scientific notation, 280 billion can be expressed as \(2.8 \times 10^{11}\).

However, since the answer choices are given in a slightly different form, we assess the closest option. The only option that represents the value reasonably well in scientific notation is:

• 2.79 × 10^11

This is very close to our estimate \(2.8 × 10^{11}\) when rounded to a single digit.

Therefore, the closest estimation of the federal debt of Country C is:

2.79 × 10^11