4.44444444444 as a Fraction

Professor Greenline Explaining Math Concepts

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Intermediate

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Numbers can be categorized into different types. Fraction is one of its kind. 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; the numbers in decimal are expressed with a decimal point (.), For example, 4.44444444444. We are going to learn how to convert a decimal to a fraction.

What is 4.44444444444 as a Fraction?

$4.44444444444 as a fraction$

Answer

The answer for 4.44444444444 as a fraction is 40/9.

Explanation

Converting a repeating decimal to a fraction involves a few steps that allow us to express the repeating part as a fraction. You can follow the steps mentioned below to find the answer.

Step 1: Let x be the repeating decimal 4.44444444444..., which we can write as: x = 4.44444444444...

Step 2: Multiply x by 10 to shift the decimal point one place to the right, as the repeating part (4) is one digit long: 10x = 44.4444444444...

Step 3: Subtract the original equation from this new equation to eliminate the repeating part: 10x - x = 44.4444444444... - 4.44444444444...

Step 4: Simplify the equation: 9x = 40

Step 5: Solve for x by dividing both sides by 9: x = 40/9

Thus, 4.44444444444 can be written as a fraction 40/9.

Important Glossaries for 4.44444444444 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.
Repeating Decimal: A decimal in which a sequence 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.