10 2/3 as a Decimal

Professor Greenline Explaining Math Concepts

Foundation

Intermediate

Advance Topics

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, numerator (number on the top) here, 2 represents how many parts out of the whole. The denominator (number below) shows how many parts make the whole, here it is 3. A decimal is a way to represent the number that is not whole, using a (.) or a decimal to separate the whole part from the fraction part. The numbers to the left of the decimal point represent the whole, and that to the right represents the fractional part.

What is 10 2/3 as a decimal?

$10 2/3 as a decimal$

Answer

10 2/3 in decimal can be written as 10.66666….. It is a recurring decimal, showing it will repeat the same digit infinitely.

Explanation

To convert 10 2/3 to decimal, we will separate the whole number and the fractional part. The whole number is 10. For 2/3, we will use the division method. Let's see the step-by-step breakdown of the process:

Step 1: Identify the numerator and denominator because numerator (2) will be taken as dividend and denominator (3) will be taken as divisor.

Step 2: As 2 is smaller than 3, it can't be divided. Here we will take the help of decimals. We will add 0 to the dividend, which will make 2 as 20 and add a decimal point in the quotient place.

Step 3: Now that it is 20, we can divide it by 3. Let's see how many times 3 makes 20.

Step 4: 20 is not a multiple of 3, so we will look for the nearest number that is 3 × 6 = 18. We will write 6 in the quotient place and subtract 18 from 20, giving us 2.

Step 5: Bring down another 0 in the dividend place and make 2 as 20, then repeat the division process. The division process continues, and we don't get the remainder as 0. This process is called a recurring decimal.

The answer for 10 2/3 as a decimal will be 10.6666……