1.1
The Number System
July 17, 2025
Shivohm Karogal
1
Min Read
AI Summary
These revision notes explain how to convert recurring decimals into fractions using algebraic manipulation. By assigning a variable to the repeating decimal, multiplying by a power of 10, subtracting the original equation, and solving for the variable, students can express repeating decimals like 0.83̅ as exact fractions, such as 83/99.
Objective
Develop the ability to convert irrational or recurring decimals to fractions through algebraic manipulation.
Core Concept
While many decimals can be converted into fraction form, recurring decimals require specific algebraic techniques to express them accurately as fractions.
Expressing Repeating Decimals as Fractions
Assign a Variable: Let X = 0.83̅ (where 83 repeats).
Multiply by a Power of 10: Multiply both sides to shift the decimal:
100X = 83.83̅
Subtract the Original Equation: Subtract the original equation from this:
100X - X = 83.83̅ - 0.83̅ → 99X = 83
Solve for X: Divide both sides by 99:
X = 83/99