Set the decimal equal to a variable.

Question

ScanSolve AI Tutor · Accepted Answer

Here's how to write the decimal number 0.8333333... as a rational number:

Set the decimal equal to a variable.
Let $x = 0.8333333...$ (Equation 1)
Multiply to shift the non-repeating part to the left of the decimal point.
The non-repeating part is '8'. Multiply Equation 1 by 10. $10x = 8.3333333...$ (Equation 2)
Multiply to shift one full repeating block to the left of the decimal point.
The repeating digit is '3'. Multiply Equation 2 by 10. $100x = 83.3333333...$ (Equation 3)
Subtract Equation 2 from Equation 3 to eliminate the repeating decimal part.
$100x - 10x = 83.3333333... - 8.3333333...$ $90x = 75$
Solve for $x$ .
$x = \frac{75}{90}$
Simplify the fraction.
Both the numerator and the denominator are divisible by 15.
$x = \frac{75 \div 15}{90 \div 15} = \frac{5}{6}$
The decimal number 0.8333333... as a rational number is:
$\mathbf{\frac{5}{6}}$

Answer