1.58333333333 as a Fraction

Professor Greenline Explaining Math Concepts

Numbers can be categorized into different types. A fraction is one such type. It is always represented in the form of p/q, where p is the numerator and q is the denominator. A fraction represents both a whole and a fractional part. Decimals represent the fractional part of numbers. For example, 1/2; numbers in decimal form are expressed with a decimal point (.), such as 1.58333333333. We are going to learn how to convert this repeating decimal to a fraction.

1.58333333333 as a Fraction for US Students

What is 1.58333333333 as a Fraction?

$1.58333333333 as a fraction$ Answer

The answer for 1.58333333333 as a fraction will be 19/12.

Explanation

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

Step 1: Let x be the repeating decimal, so x = 1.58333333333...

Step 2: Identify the repeating part, which is '3', and write the decimal as 1.5 + 0.08333333333...

Step 3: Convert the non-repeating part, 1.5, to a fraction. 1.5 = 3/2.

Step 4: For the repeating part, let y = 0.08333333333..., then 10y = 0.8333333333... Subtract y from 10y: 10y - y = 0.8333333333... - 0.0833333333... 9y = 0.75 y = 0.75/9 = 1/12

Step 5: Add the fractions from the non-repeating and repeating parts. 3/2 + 1/12 = 18/12 + 1/12 = 19/12

Thus, 1.58333333333 can be written as a fraction 19/12.

Important Glossaries for 1.58333333333 as a Fraction

Fraction: A numerical quantity that is not a whole number, representing a part of a whole.
Repeating Decimal: A decimal in which a digit or group of digits repeats infinitely.
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.
Mixed Number: A whole number combined with a fraction, often used to express numbers greater than one in a more readable form.