Convert 5.5 (with a bar notation above the 5)
Into a decimal
The bar notation above the 5 in 5.5 indicates that the digit 5 is repeated indefinitely. To convert this to a decimal, we can represent it as a fraction.
Let x = 5.55555...
Multiply both sides of the equation by 10 to remove the decimal:
10x = 55.55555...
Now, subtract the original equation from the previous equation to eliminate the repeating decimal:
10x - x = 55.55555... - 5.55555...
= 50
Simplifying the equation:
9x = 50
Now divide both sides of the equation by 9:
x = 50/9
Therefore, 5.5 (with a bar notation above the 5) is equivalent to the decimal 50/9.
To convert a number with a bar notation above it into a decimal, we can use the following steps:
Step 1: Write the given number as an equation with x equal to the repeating decimal part:
5.5 with a bar notation above the 5 can be written as 5.55... = x
Step 2: Multiply both sides of the equation by 10 to move the decimal point one place to the right:
10x = 55.55...
Step 3: Subtract the original equation from the equation obtained in step 2 to eliminate the repeating decimal part:
10x - x = 55.55... - 5.55...
Simplifying, we get:
9x = 50
Step 4: Divide both sides of the equation by 9 to solve for x:
9x/9 = 50/9
Simplifying, we get:
x ≈ 5.555...
Therefore, the decimal representation of 5.5 with a bar notation above the 5 is approximately 5.555.