1.2(4)
* 4 is recurring
changing 1.2(4) into a fraction in the form a/b
1.244444...
= 1 + .24444....
= 1 + (24-2)/90
= 1 + 22/90
= 1 + 11/45
= 56/45
check with a calculator, it is correct
or
let x = 1.244444
time 10
10x = 12.4444...
x = 1.244444.
--------------
subtract:
9x = 11.2
x = 11.2/9
= 112/90
= 56/45
To solve 1.2(4) with the recurring 4, we need to understand the concept of recurring decimals or repeating decimals.
In this case, the number 1.2(4) means that the digit 4 after the decimal point repeats indefinitely. To represent it as a fraction in the form a/b, we can use algebraic manipulation.
Let's assign a variable to the recurring decimal:
Let x = 1.2(4)
Now, we can multiply x by a power of 10 to eliminate the repeating part. Since there is one digit repeating, we will multiply x by 10 to get:
10x = 12.(4)
Next, we subtract x from 10x:
10x - x = 12.(4) - 1.2(4)
This simplifies to:
9x = 12
Now, we can solve for x by dividing both sides of the equation by 9:
x = 12/9
To further simplify, we can divide both the numerator and denominator by their greatest common divisor, which is 3:
x = 4/3
Therefore, the value of 1.2(4) expressed as a fraction in the form a/b is 4/3.