5 2/3 as a Decimal

Answer

5 2/3 in decimals can be written as 5.66666… It is a recurring decimal, indicating that the digit 6 repeats infinitely.

Explanation

To convert 5 2/3 into a decimal, start by converting the fractional part (2/3) into a decimal. We will use the division method for this.

Step 1: Identify the numerator (2) and the denominator (3). The numerator will be the dividend, and the denominator will be the divisor.

Step 2: As 2 is smaller than 3, we will use decimals to proceed with the division. We add a decimal in the quotient and a zero to the dividend, making it 20.

Step 3: Divide 20 by 3. The closest multiple of 3 to 20 is 18 (3 × 6), so we place 6 in the quotient. Subtract 18 from 20 to get a remainder of 2.

Step 4: Bring down another 0 to make 2 into 20, then repeat the division process. This process continues, and the remainder never reaches 0, resulting in a recurring decimal for 2/3, which is 0.6666…

Finally, add this to the whole number 5, giving us 5.6666… as the decimal representation of 5 2/3.

• Mixed Number: A whole number and a fraction combined into one "mixed" number.

• 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.

• Recurring Decimal: A decimal fraction that has one or more repeating digits or sequence of digits following the decimal point.

• Division Method: A mathematical process to convert fractions into decimals by dividing the numerator by the denominator.