Rewrite as a simplified fraction 1.5 (5 repeating)
To rewrite 1.5 (5 repeating) as a simplified fraction, we can use the fact that 0.5 (5 repeating) can be expressed as 1/2. Therefore, 1.5 (5 repeating) can be written as:
1.5 (5 repeating) = 1 + 0.5 (5 repeating)
= 1 + 1/2
= 2/2 + 1/2
= 3/2
To rewrite the decimal 1.5 (5 repeating) as a simplified fraction, let's call it x:
x = 1.5555...
To get rid of the repeating decimal, we can multiply both sides of the equation by 10 to move the decimal one place to the right:
10x = 15.5555...
Then, we subtract the original equation from the equation after multiplying by 10:
10x - x = 15.5555... - 1.5555...
Simplifying the equation:
9x = 14
Dividing both sides of the equation by 9:
x = 14/9
Therefore, the simplified fraction form of 1.5 (5 repeating) is 14/9.
To rewrite the decimal 1.5 (5 repeating) as a simplified fraction, we first need to understand the repeating decimal notation. When a digit or sequence of digits repeats indefinitely, it is denoted by placing a bar over the repeating part. In this case, the decimal is 1.5 followed by the digit 5 repeating infinitely, so we write it as 1.5̅.
To convert this repeating decimal to a fraction, we'll use an algebraic trick. Let's assume x = 1.55̅ as a decimal.
Now, we can multiply both sides of the equation by a power of 10 to shift the decimal point to eliminate the repeating part. Since there is only one digit repeating, we can multiply by 10 to eliminate the repeating part:
10x = 15.55̅
Next, we can subtract x from 10x:
10x - x = 15.55̅ - 1.55̅
This simplifies to:
9x = 15
Now, we can solve for x by dividing both sides of the equation by 9:
x = 15 / 9
Simplifying the fraction 15/9, we find that it can be reduced to 5/3.
Therefore, the fraction representation of 1.5 (5 repeating) is 5/3.