Question

How do you write the simple fraction equivalent of $1.56$?

Answer 1

Hint: Here, we are required to write the simple fraction which is equal to the given decimal number. Thus, we will write this decimal number as a sum of whole numbers and a fraction and then, simplify it further to find a mixed fraction which can be further converted to the required improper or the simple fraction of the given decimal number.

Complete step by step solution:
In order to convert the given decimal number $1.56$ to a simple fraction, we can first of all write this decimal number as:
$1.56 = 1 + \dfrac{{56}}{{100}}$
This is because the number 56 is present after the decimal point and hence, its place value is one hundredths.
Thus, we have divided it by 100.
Now, we will do the prime factorization of 56 and 100.
Hence, we know,
$56 = 2 \times 2 \times 2 \times 7$
$100 = 2 \times 2 \times 5 \times 5$
Thus, we can write $1.56 = 1 + \dfrac{{56}}{{100}}$ as:
$1.56 = 1 + \dfrac{{2 \times 2 \times 2 \times 7}}{{2 \times 2 \times 5 \times 5}}$
Now, cancelling out the like terms from the numerator and denominator, we get,
$1.56 = 1 + \dfrac{{2 \times 7}}{{5 \times 5}} = 1 + \dfrac{{14}}{{25}}$
Thus, we get the mixed fraction:
$1.56 = 1\dfrac{{14}}{{25}}$
In order to convert a mixed fraction to a simple or improper fraction, we multiply the denominator by the whole number and add this to the numerator and write the result as the new numerator.
Thus, we get,
$1.56 = \dfrac{{1 \times 25 + 14}}{{25}} = \dfrac{{39}}{{25}}$

Therefore, the simple fraction equivalent of $1.56$ is $\dfrac{{39}}{{25}}$
Hence, this is the required answer.

Note:
Alternatively, we can simply write the given decimal number $1.56$ as a fraction.
As we can observe, the decimal point is after two digits.
Thus, we will add two zeros in the denominator.
Hence, we get,
$1.56 = \dfrac{{156}}{{100}}$
Now, we will find the prime factorization of the numerator and the denominator.
Thus, we get,
$156 = 2 \times 2 \times 3 \times 13$
$100 = 2 \times 2 \times 5 \times 5$
Thus, substituting these products of factors in the numerator and the denominator, we get,
$1.56 = \dfrac{{2 \times 2 \times 3 \times 13}}{{2 \times 2 \times 5 \times 5}}$
Now, cancelling out the like terms from the numerator and denominator, we get,
\[1.56 = \dfrac{{3 \times 13}}{{5 \times 5}} = \dfrac{{39}}{{25}}\]
Therefore, the simple fraction equivalent of $1.56$ is $\dfrac{{39}}{{25}}$
Hence, this is the required answer.