Bolton Huff
01/01/2024 · Senior High School
Graded Quiz: Decimals Graded Quiz: Decimals If the following fractions were converted to decimals, which one would result in a repeating decimal?
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Step-by-step Solution
To determine which fractions would result in a repeating decimal when converted to decimals, we need to consider the properties of fractions. A fraction will result in a repeating decimal if its denominator (when in simplest form) has prime factors other than 2 and 5.
Here are some examples of fractions and their analysis:
1. **1/2** - Decimal: 0.5 (terminating)
2. **1/4** - Decimal: 0.25 (terminating)
3. **1/5** - Decimal: 0.2 (terminating)
4. **1/3** - Decimal: 0.333... (repeating)
5. **1/6** - Decimal: 0.1666... (repeating)
6. **1/7** - Decimal: 0.142857... (repeating)
7. **1/8** - Decimal: 0.125 (terminating)
8. **1/9** - Decimal: 0.111... (repeating)
From this analysis, fractions like **1/3**, **1/6**, **1/7**, and **1/9** would result in repeating decimals.
If you have specific fractions in mind, please provide them, and I can help you determine which one results in a repeating decimal.
Quick Answer
Fractions like 1/3, 1/6, 1/7, and 1/9 result in repeating decimals.
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