1.714285714 as a Fraction

Professor Greenline Explaining Math Concepts

Numbers can be categorized into different types. A fraction is one of its kinds. It is always represented in the form of p/q, where p is the numerator and q is the denominator. A fraction represents a whole and a fractional part. Decimals represent the fractional part of numbers. For example, 1/2; numbers in decimal are expressed with a decimal point (.), such as 0.375. We are going to learn how to convert a decimal, specifically 1.714285714, to a fraction.

1.714285714 as a Fraction for US Students

What is 1.714285714 as a Fraction?

$1.714285714 as a fraction$ Answer

The answer for 1.714285714 as a fraction will be 12/7.

Explanation

Converting a decimal to a fraction can be straightforward if you follow the steps below.

Step 1: Firstly, any decimal number can be converted to a fraction for easy calculation. Here, 1.714285714 is the decimal. To express this as a fraction, consider the repeating decimal part. 1.714285714 is the same as 1 + 0.714285714.

Step 2: Recognize that 0.714285714 is a repeating decimal. The repeating part is 714285, which repeats every 6 digits. To convert this to a fraction, set x = 0.714285714. Multiply both sides by 10^6 (since it repeats every 6 digits) to get 1000000x = 714285.714285714.

Step 3: Subtract x from 1000000x to eliminate the repeating part: 1000000x - x = 714285.714285714 - 0.714285714 999999x = 714285 x = 714285/999999

Step 4: Simplify the fraction. The greatest common divisor (GCD) of 714285 and 999999 is 142857, so 714285/999999 = 5/7

Step 5: Therefore, 0.714285714 as a fraction is 5/7. Adding the whole number part: 1 + 5/7 = 12/7

Thus, 1.714285714 can be written as the fraction 12/7.

Important Glossaries for 1.714285714 as a Fraction

Fraction: A numerical quantity that is not a whole number, representing a part of a whole.
Decimal: A number that uses the base ten and includes a decimal point to separate the whole part from the fractional part.
Numerator: The top part of a fraction, indicating how many parts of the whole are being considered.
Denominator: The bottom part of a fraction, showing how many parts make up a whole.
Repeating Decimal: A decimal fraction in which a figure or group of figures is repeated indefinitely.