Fractions and decimals are two distinct ways of representing numerical values. Fractions consist of a numerator (the top number) and a denominator (the bottom number), separated by a division line. Decimals, on the other hand, are written in two parts: the whole numbers part and the decimals part, separated by a decimal point. Converting fractions to decimals is a fundamental mathematical operation that finds applications in various fields. This article delves into the conversion of the fraction 1/14 to a decimal using the long division method.
Understanding Fractions and Decimals
In a fraction, the numerator represents the number of parts taken from a whole, while the denominator indicates the total number of parts in the whole. For instance, in the fraction 1/14, the numerator 1 signifies that one part is taken, and the denominator 14 indicates that the whole is divided into 14 equal parts.
Decimals, on the other hand, are expressed using a base-10 system. The digits to the left of the decimal point represent the whole numbers, while the digits to the right of the decimal point represent the fractional parts. For example, the decimal 0.75 represents 75 hundredths, which is equivalent to the fraction 75/100.
Converting 1/14 to a Decimal Using the Long Division Method
The long division method is a widely used technique for converting fractions to decimals. This method involves dividing the numerator by the denominator, resulting in a quotient, remainder, and possibly a repeating or terminating decimal.
Step 1: Set Up the Division
To initiate the long division process, set up the division as follows:
“`
1 ÷ 14
“`
Place the numerator 1 as the dividend and the denominator 14 as the divisor. Draw a horizontal line below the dividend and place the decimal point above the line, directly above the division symbol.
Step 2: Perform the Division
Begin the division process by dividing the first digit of the dividend (1) by the first digit of the divisor (1). This results in a quotient of 0.
“`
0.
1 ÷ 14
“`
Next, multiply the divisor (14) by the quotient (0) and write the product (0) below the dividend. Subtract the product from the dividend to obtain the remainder (1).
“`
0.
1 ÷ 14
-0
1
“`
Bring down the next digit of the dividend (0) and place it next to the remainder (1). This forms the new dividend (10).
Step 3: Continue the Division Process
Repeat the division process by dividing the new dividend (10) by the divisor (14). This results in a quotient of 0.
“`
0.0
10 ÷ 14
-0
10
“`
Multiply the divisor (14) by the quotient (0) and write the product (0) below the new dividend. Subtract the product from the new dividend to obtain the remainder (10).
“`
0.0
10 ÷ 14
-0
10
-0
10
“`
Bring down the next digit of the dividend (0) and place it next to the remainder (10). This forms the new dividend (100).
Step 4: Continue Until the Remainder is Zero or Repeats
Continue the division process until the remainder becomes zero or starts repeating. In the case of 1/14, the division process will continue indefinitely, resulting in a non-terminating, repeating decimal.
“`
0.07142857142857…
100 ÷ 14
-98
2
-2
0
10
-98
2
…
“`
The repeating pattern of digits is 142857. Therefore, the decimal representation of 1/14 is 0.07142857142857…, where the digits 142857 repeat infinitely.
Conclusion
In conclusion, converting 1/14 to a decimal using the long division method results in a non-terminating, repeating decimal of 0.07142857142857…. This conversion process demonstrates the relationship between fractions and decimals and highlights the significance of understanding the underlying principles of number representation.
References
* [What is 1/14 as a decimal? | Thinkster Math](https://hellothinkster.com/math-questions/decimals/what-is-1-14-as-a-decimal)
* [What Is 1/14 as a Decimal + Solution With Free Steps](https://www.storyofmathematics.com/fractions-to-decimals/1-14-as-a-decimal/)
* [How do you convert 1 14 to a decimal and in to a percent? – Answers](https://math.answers.com/basic-math/How_do_you_convert_1_14_to_a_decimal_and_in_to_a_percent)
FAQs
What is the decimal representation of 1/14?
0.07142857142857… (non-terminating, repeating decimal)
Why does 1/14 result in a non-terminating, repeating decimal?
When the numerator (1) is divided by the denominator (14) using the long division method, the division process continues indefinitely without reaching a remainder of zero. This results in a decimal that never terminates and instead repeats a specific pattern of digits infinitely.
How can I perform the long division to convert 1/14 to a decimal?
To perform the long division, follow these steps:
– Set up the division with the numerator as the dividend and the denominator as the divisor.
– Divide the first digit of the dividend by the first digit of the divisor to obtain the quotient.
– Multiply the divisor by the quotient and write the product below the dividend.
– Subtract the product from the dividend to obtain the remainder.
– Bring down the next digit of the dividend and repeat the process until the remainder becomes zero or starts repeating.
What is the significance of converting fractions to decimals?
Converting fractions to decimals is significant because it allows for easier comparison, calculation, and manipulation of numerical values. Decimals are widely used in various fields, including science, engineering, finance, and everyday life, making it essential to understand how to convert between fractions and decimals.
Are there any other methods to convert 1/14 to a decimal?
Yes, there are alternative methods to convert 1/14 to a decimal. One method involves using a calculator with a division function. Simply enter 1 divided by 14 and the calculator will display the decimal result. Another method involves expressing 1/14 as a percentage and then converting the percentage to a decimal.
What is the practical application of converting 1/14 to a decimal?
Converting 1/14 to a decimal has practical applications in various fields. For example, in carpentry, it is useful for precise measurements and calculations involving fractions of an inch. In cooking, it is helpful for accurately measuring ingredients when following recipes that use fractional amounts. Additionally, in finance, it is essential for calculating percentages, interest rates, and other financial computations.
Can 1/14 be expressed as a terminating decimal?
No, 1/14 cannot be expressed as a terminating decimal. A terminating decimal is a decimal that has a finite number of digits after the decimal point. Since the decimal representation of 1/14 is non-terminating, it cannot be expressed as a terminating decimal.
What is the repeating pattern of digits in the decimal representation of 1/14?
The repeating pattern of digits in the decimal representation of 1/14 is 142857. This pattern repeats infinitely after the decimal point, resulting in a non-terminating, repeating decimal.