46 2/3 as a Decimal

Answer

46 2/3 in decimals can be written as 46.66666….. It is a recurring decimal, indicating it will repeat the same digit infinitely.

Explanation

To express 46 2/3 as a decimal, we will first convert the fractional part 2/3 into a decimal using division. Then, we'll add this to the whole number 46. Let's see the step-by-step breakdown of the process:

Step 1: Identify the numerator and denominator of the fraction 2/3. Here, the numerator (2) will be taken as the dividend, and the denominator (3) will be the divisor.

Step 2: As 2 is smaller than 3, it can't be divided without a remainder. We will use the decimal method by adding 0 to the dividend, making it 20, and adding 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 fits into 20.

Step 4: 20 is not a multiple of 3, so we will find the nearest number, which is 3 × 6 = 18. We will write 6 in the quotient place and subtract 18 from 20, leaving 2.

Step 5: Bring down another 0 in the dividend place to make it 20 again, and repeat the division process. The division process continues as the remainder never becomes 0, resulting in a recurring decimal. Thus, 2/3 as a decimal is 0.6666..., and when added to the whole number 46.

The result is 46.6666…

• 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.

• Recurring Decimal: A decimal in which a sequence of digits repeats infinitely.