The calculation of 5 divided by 7 is a straightforward mathematical operation that yields a specific result. To perform this calculation, we simply divide the numerator, 5, by the denominator, 7. The result of this calculation is approximately 0.71428571. However, it's essential to note that this is a repeating decimal, where the sequence "714285" repeats infinitely.
Exact Fractional Representation
The exact result of 5 divided by 7 can be represented as a fraction, which is 5⁄7. This fractional representation provides a precise and concise way to express the result of the calculation without resorting to decimal approximations. The fraction 5⁄7 is an irreducible fraction, meaning that the numerator and denominator have no common factors other than 1.
Repeating Decimal Expansion
As mentioned earlier, the decimal expansion of 5⁄7 is a repeating decimal. The repeating pattern “714285” can be observed when dividing 5 by 7 using long division. This repeating pattern is a characteristic of rational numbers, which are numbers that can be expressed as the ratio of two integers. In this case, the rational number 5⁄7 has a repeating decimal expansion that reflects its fractional nature.
| Calculation | Result |
|---|---|
| 5 ÷ 7 | 0.71428571 (repeating) |
| Exact Fractional Representation | 5/7 |
Key Points
- The result of 5 divided by 7 is approximately 0.71428571, which is a repeating decimal.
- The exact result can be represented as the fraction 5/7, which is an irreducible fraction.
- The repeating decimal expansion of 5/7 reflects its rational nature and can be observed using long division.
- Understanding fractions and their decimal expansions is essential for developing a deep appreciation for mathematical relationships and calculations.
- The calculation of 5 divided by 7 serves as a fundamental example of how fractions can be used to represent precise mathematical relationships.
In conclusion, the calculation of 5 divided by 7 yields a result that can be represented as a fraction or a repeating decimal. By understanding the properties of fractions and their decimal expansions, we can gain insight into the underlying structure of mathematics and develop a deeper appreciation for the intricacies of numerical calculations. The result of this calculation has numerous applications in various mathematical contexts, including algebra, geometry, and calculus.
What is the exact result of 5 divided by 7?
+The exact result of 5 divided by 7 is the fraction 5⁄7, which is an irreducible fraction.
Why is the decimal expansion of 5⁄7 a repeating decimal?
+The decimal expansion of 5⁄7 is a repeating decimal because it is a rational number, which means it can be expressed as the ratio of two integers. Rational numbers often have repeating decimal expansions, as observed in the case of 5⁄7.
What are some practical applications of the calculation 5 divided by 7?
+The calculation 5 divided by 7 has numerous applications in various mathematical contexts, including algebra, geometry, and calculus. For example, it can be used to calculate proportions, ratios, and percentages in real-world problems.
