1.46666 as a Fraction

Professor Greenline Explaining Math Concepts

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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. Fractions represent 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, 1.46666, we are going to learn how to convert a decimal to a fraction.

What is 1.46666 as a Fraction?

$1.46666 as a fraction$

Answer

The answer for 1.46666 as a fraction will be 22/15.

Explanation

Converting a decimal to a fraction is a task for students that can be done easily. You can follow the steps mentioned below to find the answer.

Step 1: Firstly, any decimal number should be converted to a fraction for easy calculation. Here, 1.46666 is the number on the numerator and the base number 1 will be the denominator. Then, 1.46666 becomes 1.46666/1.

Step 2: To remove the repeating decimal from the fraction, recognize that 1.46666... is equivalent to 1.46 with the 6 repeating. Consider it as 1.46 + 0.00666....

Step 3: Express the repeating decimal part. Let x = 0.00666..., then 10x = 0.0666... and 100x = 0.6666.... Thus, 100x - 10x = 0.6666... - 0.0666..., which simplifies to 90x = 0.6, so x = 0.6/90 = 1/150. Therefore, 0.00666... = 1/150.

Step 4: Add this to the non-repeating part. 1.46 as a fraction is 146/100. So, 1.46666... = 146/100 + 1/150.

Step 5: Find a common denominator for 146/100 and 1/150, which is 1500. Convert each fraction: 146/100 = 2190/1500 and 1/150 = 10/1500.

Step 6: Add the fractions: 2190/1500 + 10/1500 = 2200/1500. Simplify by dividing the numerator and denominator by their GCD, which is 100. This gives 22/15.

Thus, 1.46666 can be written as a fraction 22/15.