Consider the following statements
(A) The difference between the place values of 9 and 5 in the number 639457 is 4.
(B) The number \(\pi\) is an irrational number.
(C) The sum of all the prime numbers from 1 to 20 is 67.
(D) The difference between the face values of 5 and 3 in number 475839 is 2.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B) and (D) only
The face value of a digit is the digit itself. Its place value is the digit multiplied by the value of its place (ones, tens, hundreds, …).
(A) The difference between the place values of 9 and 5 in the number 639457 is 4. Incorrect. In 639457 the 9 is in the thousands place and the 5 in the tens place, so their place values are 9000 and 50, and the difference is \(9000-50=8950\). The 4 is the difference of their face values.
(B) The number \(\pi\) is an irrational number. Correct. \(\pi\) cannot be written as a fraction \(\frac{p}{q}\) of two integers; its decimal form 3.14159… never ends and never repeats. The value \(\frac{22}{7}\) is only an approximation.
(C) The sum of all the prime numbers from 1 to 20 is 67. Incorrect. The primes up to 20 are 2, 3, 5, 7, 11, 13, 17 and 19 (1 is not a prime), and their sum is \(2+3+5+7+11+13+17+19=77\), not 67.
(D) The difference between the face values of 5 and 3 in number 475839 is 2. Correct. Face values do not depend on the place, so the difference is \(5-3=2\).