5/7 as a Decimal

Professor Greenline Explaining Math Concepts

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It is a simple question on decimal conversion. Firstly, we have to learn fractions and decimals. A fraction represents a part from the whole. It has two parts: the numerator (number on the top), here 5, which represents how many parts out of the whole. The denominator (number below) shows how many parts make the whole, here it is 7. A decimal is a way to represent a number that is not whole, using a (.) or a decimal to separate the whole part from the fractional part. The numbers to the left of the decimal point represent the whole, and those to the right represent the fractional part.

What is 5/7 as a decimal?

$5/7 as a decimal$

Answer

5/7 in decimals can be written as approximately 0.714285. It is a repeating decimal, showing that the sequence 714285 will repeat infinitely.

Explanation

To convert 5/7 into a decimal, we will use the division method. Since 5 is smaller than 7, we will use the decimal method which provides us with 0.714285.

Let's see a step-by-step breakdown of the process:

Step 1: Identify the numerator and denominator because the numerator (5) will be taken as the dividend and the denominator (7) will be taken as the divisor.

Step 2: Since 5 is smaller than 7, it cannot be divided. We will use decimals by adding 0 to the dividend, making it 50, and placing a decimal point in the quotient position.

Step 3: Now that it's 50, we can divide by 7. Let's see how many times 7 fits into 50.

Step 4: 50 is not a multiple of 7, so we look for the nearest number, which is 7 × 7 = 49. We write 7 in the quotient and subtract 49 from 50, which gives 1.

Step 5: Bring down another 0 in the dividend position to make it 10, then repeat the division process. The division process continues, and it does not result in a remainder of 0. This process results in a repeating decimal.

The answer for 5/7 as a decimal is approximately 0.714285...

Important Glossaries for 5/7 as a decimal

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 in which a sequence of digits repeats infinitely.