Question

How do you write \[\dfrac{{43}}{{100}}\] in decimal?

Answer 1

Hint: Here, we need to express the given fraction as a decimal. First, we will write the fraction in simplest form if possible. Then, we will rewrite the fraction into decimal by dividing the numerator by the denominator. A decimal number is a number which contains a whole number part and a fractional part separated by a decimal point.

Complete step-by-step answer:
A fraction is a number which represents a part of a group. It is written as \[\dfrac{a}{b}\], where \[a\] is called the numerator and \[b\] is called the denominator. The group is divided into \[b\] equal parts. The fraction \[\dfrac{a}{b}\] represents \[a\] out of \[b\] equal parts of the group.
First, we will write the given fraction in the simplest form.
The numerator of the fraction \[\dfrac{{43}}{{100}}\] is 43 and the denominator is 100.
Since 43 and 100 are not divisible by any same number, we cannot simplify the fraction further.
Thus, 43 and 100 are co-prime numbers.
The given fraction \[\dfrac{{43}}{{100}}\] is in its simplest form.
Now, we will convert the fraction in simplest form to decimal.
We will divide 43 by 100 to get the required decimal.
Dividing 43 by 100, we get the decimal number
\[ \Rightarrow \dfrac{{43}}{{100}} = 0.43\]
Therefore, we have expressed the fraction \[\dfrac{{43}}{{100}}\] as the decimal \[0.43\].

Additional information:
We used the term co-prime numbers in the solution. Two numbers are called co-prime numbers if they do not share a common factor other than 1. For example, the factors of 43 are 1 and 43. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. We can observe that 43 and 100 are co-prime since they have no common factor other than 1.

Note: We divided 43 by 100 in the solution. The quotient of a number by a power of 10 (10, 100, 1000, etc) can be calculated using a simple method. The number of zeros in 100 is 2. When a number is divided by 100, the result can be obtained by shifting the decimal point 2 digits to the left from the last digit. For example: The number 43 can be written as 043. When 043 is divided by 100, the result is \[0.43\], which is simply obtained by shifting the decimal point two places to the left from the last digit 3.