4 cm = 40mm，40×3-(3- 1)×2×5 = 120-20 = 100(mm)= 10(cm)。 So the total length after tensioning is 10 cm.

According to the meaning of the question, there are overlapping parts in the middle of iron rings, and the number of overlapping times is equal to twice the number of iron rings minus 1, that is, (3- 1)×2. The length of each overlap is 5 mm of the thickness of the iron ring, and the overlap length can be calculated by multiplication first. Next, multiply the length of each iron ring by the number of iron rings 3, and then subtract the length of the overlapping part to find the length of the connection, paying attention to the unified unit.

This problem belongs to the problem of examining the compound application of integers. The key to solve this problem is to master the conversion between centimeters and millimeters. An integer compound application problem is a quantitative relationship in which there are two or more interrelated problems.

To find out the relationship between the known quantity and the unknown quantity according to the interrelated quantitative relationship, we must first solve one or several intermediate problems, that is, combine two or more interrelated simple application problems.

The importance of learn mathematics:

1. Mathematics is closely related to our life. To say that the real effect of learning mathematics is not reflected in exam-oriented education, but in my own thinking about the future.

2. The importance of mathematics is self-evident. Mathematics is the foundation of all sciences and an important channel to cultivate logical thinking. It can be said that every major progress of our mankind is strongly supported by mathematics.

3. The application of mathematical knowledge in life is everywhere. From the calculation of daily living costs, to astronomy, geography, quality control, agricultural economy, aerospace, there are shadows of using mathematics.