3 4/7 as a Decimal

Answer

3 4/7 in decimals can be written as 3.5714285….. It is a recurring decimal, showing it will repeat the sequence of digits infinitely.

Explanation

To convert 3 4/7 into a decimal, we will first convert the fractional part 4/7 into a decimal using the division method and then add it to the whole number 3. Let's see the step-by-step breakdown of the process:

Step 1: Identify the numerator and denominator of the fractional part, where the numerator (4) will be taken as the dividend and the denominator (7) will be taken as the divisor.

Step 2: Since 4 is smaller than 7, it can't be divided directly; here, we will take the help of decimals. We will add 0 to the dividend, making it 40, and add a decimal point in the quotient place.

Step 3: Now that it is 40, we can divide it by 7. Let's see how many times 7 fits into 40.

Step 4: 40 is not a multiple of 7, so we will look for the nearest number that is 7 × 5 = 35. We write 5 in the quotient place and subtract 35 from 40 to get 5.

Step 5: Bring down another 0 in the dividend place, making it 50, and then repeat the division process. The division process continues with recurring results, and we do not get a remainder of 0. This process is called a recurring decimal. Finally, add the whole number 3 to the decimal obtained from 4/7.

The answer for 3 4/7 as a decimal will be 3.5714285……

• Mixed Number: A number that consists of a whole number and a fraction.
   
• 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 in which a pattern of one or more digits is repeated infinitely.
   
• Division Method: A mathematical process used to convert fractions to decimals by dividing the numerator by the denominator.