Math Problem Statement
Solution
The image contains the following recurring decimals to be converted into fractions:
Let's start by converting these recurring decimals to fractions:
1. (53)
Let . Multiply by 10: Now subtract :
2. (54)
This is a terminating decimal, so:
3. (55)
Let . Multiply by 100: Now subtract :
4. (56)
Let . Multiply by 100: Now subtract :
5. (57)
Let . First express as: can be converted using the method above, where : Convert 0.1 to a fraction: Find a common denominator: Simplify:
6. (58)
Let . Multiply by 1000: Now subtract :
7. (59)
This is a terminating decimal, so:
8. (60)
Let . First express as: can be converted similarly: Convert 0.6 to a fraction: Find a common denominator: Simplify:
Would you like more details on any of these conversions, or have any other questions?
Here are 5 related questions to consider:
- How do you convert any recurring decimal into a fraction?
- What is the difference between terminating and recurring decimals?
- How do you simplify fractions to their lowest terms?
- What are the properties of repeating decimal patterns?
- Can every repeating decimal be expressed as a fraction?
Tip: Always simplify fractions after converting from decimals to ensure the result is in its simplest form.
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Math Problem Analysis
Mathematical Concepts
Recurring Decimals
Fractions
Simplification
Formulas
To convert a recurring decimal into a fraction: x = recurring decimal, Multiply by power of 10 to shift decimal places, Subtract and solve for x
Simplifying fractions: Divide numerator and denominator by greatest common divisor
Theorems
Concept of recurring decimals
Simplification of fractions
Suitable Grade Level
Grades 7-10