write -5.5 recurring as a fraction or mixed number in simplest form.
.55555 = 5/9
So, -5.5555 = -5 5/9 = -50/9
it's handy to know that .nnnnnn = n/9
It's easy to show that .55555=5/9, since if
n = .555555
10n = 5.55555
10n-n = 5.55555-.55555 = 5
9n = 5
n = 5/9
To convert -5.5 recurring to a fraction or mixed number in simplest form, we can follow these steps:
Step 1: Let x = -5.5 recurring.
Step 2: Multiply both sides of the equation by 10 to remove the recurring decimal:
10x = -55.5 recurring.
Step 3: Subtract x from both sides of the equation to eliminate the recurring decimal:
10x - x = -55.5 recurring - x.
9x = -55.5 recurring.
Step 4: Divide both sides of the equation by 9 to isolate x:
9x/9 = -55.5 recurring/9.
x = -55.5 recurring/9.
Step 5: Simplify the fraction -55.5 recurring/9:
x = -55.5 recurring/9
x = -6.1666.../9.
Step 6: To write this as a mixed number, we need to divide -6.1666... by 9:
Dividing -6.1666... by 9 gives us approximately -0.685185185...
So, the equivalent fraction or mixed number for -5.5 recurring in simplest form is approximately -0.685185185...
To convert a recurring decimal to a fraction, you need to follow these steps:
Step 1: Let x be the recurring decimal.
Step 2: Multiply x by a power of 10 to move the recurring part to the left of the decimal point. In this case, since the recurring part is 5, we can multiply x by 10 to move it to the left.
x = -5.55555...
10x = -55.55555...
Step 3: Subtract the original equation (x) from the equation obtained (10x) to eliminate the recurring part.
10x - x = -55.55555... - (-5.55555...)
= -50
Step 4: Solve for x:
10x - x = -50
9x = -50
x = -50/9
So, the recurring decimal -5.5 is equal to -50/9 as a fraction in simplest form.