Write 0.8333......as a vulgar fraction

Question

ScanSolve AI Tutor · Accepted Answer

To write the repeating decimal 0.8333... as a vulgar fraction, we can use algebra. Step 1: Let x equal the repeating decimal. x = 0.8333... Step 2: Multiply x by 10 to move the decimal point one place to the right, so that the repeating part aligns. 10x = 8.3333... Step 3: Subtract the original equation (x = 0.8333...) from the new equation (10x = 8.3333...). 10x = 8.3333... x = 0.8333... ----------------- 9x = 7.5 Step 4: Solve for x by dividing both sides by 9. x = (7.5) / 9 Step 5: To get rid of the decimal in the numerator, multiply both the numerator and the denominator by 10. x = (7.5 × 10) / (9 × 10); x = 75 / 90 Step 6: Simplify the fraction by finding the greatest common divisor (GCD) of 75 and 90. The GCD is 15. Divide both the numerator and the denominator by 15. x = 75 ÷ 15 / 90 ÷ 15; x = 5 / 6 The vulgar fraction for 0.8333... is 5/6.

Write 0.8333......as a vulgar fraction

Answer

Step-by-step solution

Let x equal the repeating decimal.

Multiply x by 10 to move the decimal point one place to the right, so that the repeating part aligns.

Subtract the original equation (x = 0.8333...) from the new equation (10x = 8.3333...).

Solve for x by dividing both sides by 9.

To get rid of the decimal in the numerator, multiply both the numerator and the denominator by 10.

Simplify the fraction by finding the greatest common divisor (GCD) of 75 and 90.

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