Question

Place value and face value are always equal for
(a) 0
(b) 10
(c) any digit
(d) 100

Answer 1

Hint: Place value is the value represented by a digit in a number on the basis of its position in the number. The face value of a digit is the digit itself.

Complete step-by-step answer:
Before proceeding with the question, we should know about place value and face value. A number is formed by grouping the digits together. So each digit has a value depending on its place like one’s place, ten’s place, etc called the place value of the digit. Whereas the face value of a digit for any place in the given number is the value of the digit itself. Face value is unchangeable and definite but place value changes according to the digit’s place.
 \[\text{Place}\,\text{value}\,\text{of}\,\text{a}\,\text{digit = face}\,\text{value}\,\text{of}\,\text{a}\,\text{digit }\!\!\times\!\!\text{ value}\,\text{of}\,\text{the}\,\text{place}.......\text{(1)}\]
So we are going to find every option’s place value using equation 1 and face value and then we will determine which option is correct.
Let’s start with option (a), the number is 0 and its face value is 0 itself according to the definition while its place value is also 0 as \[0\times 1=0\] .
Now let’s check option (b), in 10 the place value of 1 is 10 as \[1\times 10=10\] and place value of 0 is 0 as \[0\times 1=0\]. The face value of 1 is 1 and of 0 is 0.
Now let’s check option (c), here it is given any digit so we will take the number 475. The place value of 5 is 5 as \[5\times 1=5\], place value of 7 is 70 as \[7\times 10=70\] and place value of 4 is 400 as \[4\times 100=400\] . The face value of 4 is 4, 7 is 7 and 5 is 5.
Now let’s check option (d), 100. The place value of 0 is 0 as \[0\times 1=0\], place value of 0 is 0 as \[0\times 10=0\] and place value of 1 is 100 as \[1\times 100=100\]. The face value of 1 is 1, 0 is 0 and 0 is 0.
Hence the answer is option (a) as 0 is the only number whose face value and place value are equal.

Note: We need to clearly understand the definition of place value and face value. Also need to grasp the relationship between face value and place value from equation (1). And should always keep in mind that face value and place value of a single digit number is always the same.