What is 19.74888... as a Fraction?

19.748 equals 8887450 as a fraction.

How do you turn 19.748 repeating into a fraction?

Detailed Answer:

Step 1: To convert 19.748 repeating into a fraction, begin writing this simple equation:

n = 19.748 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (8) and 2 digits in the non-repeating part (74). Multiply both sides by 10³ = 1000.

1000 × n = 19748.8 (equation 2)

Step 3: Now subtract equation 1 from equation 2 to cancel the repeating block (or repetend) out.

1000 × n = 19748.8
 100 × n = 19.748
 900 × n = 17774

17774900 could be the answer, but it still can be put in the simplest form, i.e., reduced.

To simplify this fraction, divide the numerator and denominator by 2 (the GCF - greatest common factor).

n = 17774900 = 17774 ÷ 2900 ÷ 2 = 8887450. So,

19.748 = 8887450 as the lowest possible fraction.

As the numerator is greater than the denominator, we have an improper fraction, so we can also express it as a mixed number, thus 8887450 is also equal to 19337450 when expressed as a mixed number.

The repeating decimal 19.748 (vinculum notation) has a repeated block length of 1. It is also represented as 19.74888... (ellipsis notation) which equals approximately 19.7488888 (decimal approximation)(*).

The recurring decimal 19.748 can be written as a ratio of two integers having 8887 as the numerator and 450 as the denominator. So, it is a rational number (named after ratio). It can be shown that a number is rational if its decimal representation is repeating or terminating.

(*) At present, there is no single universally accepted notation or phrasing for repeating decimals.