Which decimal is equivalent to 10/3

Which decimal is equivalent to 10/3?

The Correct Answer and Explanation is:

To find the decimal equivalent of the fraction ( \frac{10}{3} ), we need to perform the division of 10 by 3.

1. Perform the Division:

• When we divide 10 by 3, we can set it up as follows:
  [
  10 \div 3
  ]
• The integer part of this division is 3, since ( 3 \times 3 = 9 ), which is the largest multiple of 3 that is less than 10.
• Subtracting 9 from 10 gives us a remainder of 1.

1. Add Decimal Places:

• To continue the division, we add a decimal point and a zero to the remainder:
  [
  10.0
  ]
• Now we can bring down the zero, making it 10 again:
  [
  10.0 \div 3 = 3.3
  ]
• Again, we see that 3 goes into 10 three times, giving us 9, with a remainder of 1.

1. Repeat the Process:

• We can keep bringing down zeros to continue this division process:
  [
  10.00 \div 3 = 3.33
  ]
• Each time we repeat this, we will continue to get 3 with a remainder of 1.

1. Recognize the Pattern:

• This means that ( \frac{10}{3} ) equals ( 3.333… ), where the digit 3 repeats indefinitely.
• Therefore, we can express ( \frac{10}{3} ) as ( 3.\overline{3} ), indicating that the 3 repeats infinitely.

1. Conclusion:

• Thus, the decimal equivalent of ( \frac{10}{3} ) is ( 3.333… ).
• This repeating decimal represents a non-terminating decimal, which is common when dealing with fractions where the denominator does not evenly divide the numerator.

In summary, ( \frac{10}{3} ) is equivalent to ( 3.333… ), or ( 3.\overline{3} ), demonstrating how certain fractions convert into repeating decimals.