Question

\(\frac {140}{210}\) is a

• A. terminating decimal
• B. non-terminating and repeating decimal
• C. non-terminating and non-repeating decimal
• D. None of the above

Answer 1

The Correct Option is B

1. The fraction \(\frac{140}{210}\) can be simplified by finding the greatest common divisor (GCD) of 140 and 210. 2. The prime factorization of 140 is: \[ 140 = 2 \times 2 \times 5 \times 7 \] The prime factorization of 210 is: \[ 210 = 2 \times 3 \times 5 \times 7 \] 3. The GCD of 140 and 210 is 70. 4. Now, divide both the numerator and the denominator by 70: \[ \frac{140}{210} = \frac{140 \div 70}{210 \div 70} = \frac{2}{3} \] So, the simplified form of \(\frac{140}{210}\) is \(\frac{2}{3}\).

This is a non-terminating and repeating decimal.

Answer 2

1. Simplify the fraction:

\(\frac{140}{210} = \frac{(140 ÷ 70)}{(210 ÷ 70) }= \frac{2}{3}\)

2. Convert to decimal:

\(\frac{2}{3} = 0.666... = 0.\overline{6} \text{(the digit 6 repeats infinitely)}\)

This is a non-terminating and repeating decimal.