Question

Write one and a quarter meter in decimals.

Answer 1

Hint:
In this question, we are required to convert ‘one and a quarter meter’ into the decimal form. To do this we write it in the mathematical or the fractional form. We then convert the fraction into a decimal by dividing the numerator with the denominator of the fraction.

Complete step by step answer:
To solve this question, we first have to write one and a quarter meter in decimals. To do this we need to know that a quarter represents one-fourth of any entity. Thus, a quarter meter is given as \[\dfrac{1}{4}\] m.
Then, one and a quarter meter can be written as \[1\dfrac{1}{4}\] m.
Now, we know that this is a mixed fraction. To solve this question further, we will need to convert this mixed fraction to the improper fraction form.
To convert \[1\dfrac{1}{4}\] m into the improper fraction form, we will add 1 and \[\dfrac{1}{4}\].
\[1\dfrac{1}{4} = 1 + \dfrac{1}{4}\]
Take the LCM of the denominators. In this case the denominators are 1 and 4, so the LCM of 1 and 4 is 4. So, we will multiply the denominators of both the terms with suitable numbers to make them 4. Subsequently, we will be multiplying the numerators with the same number too, so that the fraction does not gets altered.
\[1\dfrac{1}{4} = 1 + \dfrac{1}{4}\]
\[1\dfrac{1}{4} = \dfrac{{1 \times 4}}{{1 \times 4}} + \dfrac{{1 \times 1}}{{4 \times 1}}\]
Simplifying the above equation, we get
\[1\dfrac{1}{4} = \dfrac{4}{4} + \dfrac{1}{4}\]
As the denominators are equal, so we will add the numerator to obtain the improper fraction
\[1\dfrac{1}{4} = \dfrac{5}{4}\]
Now, we have to convert \[\dfrac{5}{4}\] to the decimal form. For this, we will divide 5 by 4.
\[\dfrac{5}{4} = 1.25\] m
Thus, the decimal form of one and a quarter meter is \[1 \cdot 25\] m.

Note:
 We can solve this question in a different way as shown below.
We know that one and a quarter meter can be written as \[1\dfrac{1}{4}\] m.
Now, we can write \[1\dfrac{1}{4}\] as given below–
\[1\dfrac{1}{4} = 1 + \dfrac{1}{4}\]
Now, divide 1 by 4.
\[1\dfrac{1}{4} = 1 + 0.25\]
Again, we will add the terms to get the required decimal form.
\[1\dfrac{1}{4} = 1.25\]
$\therefore $ The required answer is \[1.25\] m.