Fractions and decimals are two different ways of representing numbers. Fractions consist of a numerator and a denominator, separated by a horizontal line, while decimals are written using a decimal point to separate the whole number part from the fractional part. In this article, we will explore the conversion of the fraction 2/15 to its decimal representation.
Key Facts
- Decimal representation: When we convert the fraction 2/15 to a decimal, it becomes 0.133.
- Non-terminating, repeating decimal: The decimal representation of 2/15 is a non-terminating, repeating decimal. The repeating pattern or sequence, known as the repetend or reptend, is 3.
- Repeating notation: The repeating pattern can be denoted using a vinculum (overline), ellipsis (three dots), or in parentheses. In this case, it can be written as 0.1(3).
- Long division method: The long division method can be used to convert the fraction 2/15 to a decimal. By dividing 2 by 15, we get a quotient of 0.133 with a remainder of 5.
- Accuracy: To ensure accuracy, the division can be carried out to the desired decimal place. In this case, the quotient is 0.133.
Decimal Representation
When we convert the fraction 2/15 to a decimal, we obtain 0.133. This means that 2/15 is equal to 0.133, or 133 thousandths. The decimal representation of 2/15 is a non-terminating, repeating decimal. This means that the decimal digits continue infinitely, with a repeating pattern or sequence. In this case, the repeating pattern is 3.
Repeating Notation
The repeating pattern in the decimal representation of 2/15 can be denoted using various notations. One common notation is to use a vinculum (overline) above the repeating digits. In this case, we would write 0.1(3). Another notation is to use an ellipsis (three dots) after the repeating digits. In this case, we would write 0.133…. Finally, we can also use parentheses to enclose the repeating digits. In this case, we would write 0.13(3).
Long Division Method
The long division method is a commonly used technique for converting fractions to decimals. To convert 2/15 to a decimal using long division, we follow these steps:
- Write 2 as the dividend and 15 as the divisor.
- Divide 2 by 15 to obtain a quotient of 0 and a remainder of 2.
- Bring down the decimal point in the quotient.
- Multiply the remainder 2 by 10 to obtain 20.
- Divide 20 by 15 to obtain a quotient of 1 and a remainder of 5.
- Bring down the decimal point in the quotient.
- Multiply the remainder 5 by 10 to obtain 50.
- Divide 50 by 15 to obtain a quotient of 3 and a remainder of 5.
The process continues, with the remainders repeating in the same pattern. Therefore, the decimal representation of 2/15 is 0.133, with the 3 repeating infinitely.
Accuracy
To ensure accuracy in the conversion, the division can be carried out to the desired decimal place. In this case, we have carried out the division to the third decimal place, which gives us 0.133. If we were to carry out the division further, we would find that the repeating pattern continues indefinitely.
Conclusion
In summary, the fraction 2/15 is equal to the decimal 0.133. The decimal representation of 2/15 is a non-terminating, repeating decimal, with the repeating pattern being 3. The long division method can be used to convert the fraction to a decimal, and the accuracy of the conversion can be ensured by carrying out the division to the desired decimal place.
References
- https://hellothinkster.com/math-questions/decimals/what-is-2-15-as-a-decimal
- https://www.storyofmathematics.com/fractions-to-decimals/2-15-as-a-decimal/
- https://fractiontodecimal.net/two-fifteenths-in-decimal
FAQs
What is the decimal representation of 2/15?
Answer: The decimal representation of 2/15 is 0.133.
Is the decimal representation of 2/15 a terminating or repeating decimal?
Answer: The decimal representation of 2/15 is a non-terminating, repeating decimal.
What is the repeating pattern in the decimal representation of 2/15?
Answer: The repeating pattern in the decimal representation of 2/15 is 3.
How can I convert 2/15 to a decimal using long division?
Answer: To convert 2/15 to a decimal using long division, follow these steps:
- Write 2 as the dividend and 15 as the divisor.
- Divide 2 by 15 to obtain a quotient of 0 and a remainder of 2.
- Bring down the decimal point in the quotient.
- Multiply the remainder 2 by 10 to obtain 20.
- Divide 20 by 15 to obtain a quotient of 1 and a remainder of 5.
- Bring down the decimal point in the quotient.
- Continue the process until the desired decimal place is reached.
Why does the decimal representation of 2/15 repeat?
Answer: The decimal representation of 2/15 repeats because the fraction 2/15 cannot be expressed as a terminating decimal. This is because 15 is not a factor of 10, which is the base of our number system.
What is the significance of the repeating pattern in the decimal representation of 2/15?
Answer: The repeating pattern in the decimal representation of 2/15 is significant because it allows us to represent the fraction exactly. Without the repeating pattern, the decimal representation of 2/15 would be an infinite, non-repeating decimal.
Can I use a calculator to convert 2/15 to a decimal?
Answer: Yes, you can use a calculator to convert 2/15 to a decimal. Simply divide 2 by 15 using the calculator’s division function.
How can I check the accuracy of my conversion of 2/15 to a decimal?
Answer: You can check the accuracy of your conversion of 2/15 to a decimal by multiplying the decimal representation by 15. If the result is equal to 2, then your conversion is accurate.