To find the nearest whole number to the sum of 3.0035428163476343, we can simply round it to the nearest whole number. Since the decimal part .0035428163476343 is closer to 0 than to 1, the nearest whole number is 3.

Now, we need to find the numerator of the third fraction that, when added to the sum of the first two fractions, gives us the total sum of 3.0035428163476343.

Let's first calculate the sum of the first two fractions:

\[ \frac{2007}{2999} + \frac{8001}{5998} \]

To add these fractions, we need a common denominator. Since 5998 is twice 2999, we can easily find a common denominator:

\[ \frac{2007}{2999} + \frac{8001}{5998} = \frac{2007}{2999} + \frac{8001}{2 \cdot 2999} \]
\[ = \frac{2007}{2999} + \frac{8001}{2} \cdot \frac{1}{2999} \]
\[ = \frac{2007}{2999} + \frac{8001}{2 \cdot 2999} \]
\[ = \frac{2007 \cdot 2 + 8001}{2 \cdot 2999} \]
\[ = \frac{4014 + 8001}{5998} \]
\[ = \frac{12015}{5998} \]

Now, let's find the value of this sum:

\[ \frac{12015}{5998} \approx 2.0030010003334445 \]

Subtracting this value from the total sum gives us the value of the third fraction:

\[ 3.0035428163476343 - 2.0030010003334445 = 1.0005418160141898 \]

Since the denominator of the third fraction is 3999, we can find the numerator by multiplying this decimal by 3999:

\[ 1.0005418160141898 \times 3999 \approx 4001.999999999999 \]

Since we are looking for a whole number for the numerator and the result is very close to 4002, we can conclude that the numerator of the third fraction is 4002.
3.0035428163476343의 합에 가장 가까운 정수를 찾으려면 가장 가까운 정수로 반올림하면 됩니다. 소수점 .0035428163476343은 1보다 0에 더 가깝기 때문에 가장 가까운 정수는 3입니다.

이제 처음 두 분수의 합에 더하면 3.0035428163476343의 총합이 되는 세 번째 분수의 분모를 찾아야 합니다.

먼저 처음 두 분수의 합을 계산해 봅시다:

\[ \frac{2007}{2999} + \frac{8001}{5998} \]

이 분수를 더하려면 공통 분모가 필요합니다. 5998은 2999의 두 배이므로 공통 분모를 쉽게 찾을 수 있습니다:

\[ \frac{2007}{2999} + \frac{8001}{5998} = \frac{2007}{2999} + \frac{8001}{2 \cdot 2999} \]
\[ = \frac{2007}{2999} + \frac{8001}{2} \cdot \frac{1}{2999} \]
\[ = \frac{2007}{2999} + \frac{8001}{2 \cdot 2999} \]
\[ = \frac{2007 \cdot 2 + 8001}{2 \cdot 2999} \]
\[ = \frac{4014 + 8001}{5998} \]
\[ = \frac{12015}{5998} \]

이제 이 합의 값을 구해 봅시다:

\[ \frac{12015}{5998} \approx 2.0030010003334445 \]

이 값을 총합에서 빼면 세 번째 분수의 값을 구할 수 있습니다:

\[ 3.0035428163476343 - 2.0030010003334445 = 1.0005418160141898 \]

세 번째 분수의 분모가 3999이므로 이 소수를 3999로 곱하면 분모를 구할 수 있습니다:

\[ 1.0005418160141898 \times 3999 \approx 4001.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999