Question

Write $4\dfrac{1}{8}$ in decimal form and say what kind of decimal expansion it has:
(A) 4.125 Terminating
(B) 4.125 Non terminating
(C) 4.125 Repeating
(D) None

Answer 1

Hint: A number's decimal extension is its expression in base-10 (i.e., in the decimal system). Every "decimal place" in this scheme is made up of digits 0-9 grouped in such a way that each digit is multiplied by a power of 10, decreasing from left to right, and a decimal place representing the place.

Complete step by step solution:
In general, there are three forms of decimal expansion:
- Terminating
- Non-terminating Repeating
- Non-terminating Non Repeating
Decimal numbers with a finite number of digits are known as terminating decimals. For a certain number of repetitions, the number comes to an end after a decimal point.
The decimal numbers with an infinite number of digits are known as non-terminating decimals. The number would not come to an end here.
After a decimal point, repeating decimals are quantities in which a single number repeated uniformly.
There is no uniform repetition of a number of non-repeating decimals.
\[4\dfrac{1}{8} = \dfrac{{4 \times 8 + 1}}{8} = \dfrac{{33}}{8}\]

4.125 has a terminating expansion.
Decimal numbers with a finite number of digits are known as terminating decimals. For a certain number of repetitions, the number comes to an end after a decimal point.
Here the numbers came to an end after 3 decimal units.

Note:
In algebra, a decimal number is described as a number with a decimal point separating the whole number and fractional parts. A decimal point is the dot in a decimal number. The digits after the decimal point represent a number less than one.