Decimals and Fractions Write each decimal as a fraction or mixed number in simplest fort

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UpStudy AI · Accepted Answer

Sure! Converting decimals to fractions or mixed numbers involves a few straightforward steps. Below are examples illustrating how to perform these conversions and ensure the results are in their simplest form.

### **1. Converting Decimals to Fractions**

**Example 1:** Convert 0.75 to a fraction.

**Steps:**
1. **Identify the Place Value:** The decimal 0.75 has two decimal places, so it's in the hundredths place.
2. **Write as a Fraction:**  
   $$
   0.75 = \frac{75}{100}
   $$
3. **Simplify the Fraction:**  
   Find the greatest common divisor (GCD) of 75 and 100, which is 25.  
   $$
   \frac{75 ÷ 25}{100 ÷ 25} = \frac{3}{4}
   $$
   
**Answer:**  
$$
0.75 = \frac{3}{4}
$$

---

**Example 2:** Convert 0.6 to a fraction.

**Steps:**
1. **Identify the Place Value:** The decimal 0.6 has one decimal place, so it's in the tenths place.
2. **Write as a Fraction:**  
   $$
   0.6 = \frac{6}{10}
   $$
3. **Simplify the Fraction:**  
   GCD of 6 and 10 is 2.  
   $$
   \frac{6 ÷ 2}{10 ÷ 2} = \frac{3}{5}
   $$

**Answer:**  
$$
0.6 = \frac{3}{5}
$$

---

**Example 3:** Convert 0.125 to a fraction.

**Steps:**
1. **Identify the Place Value:** The decimal 0.125 has three decimal places, so it's in the thousandths place.
2. **Write as a Fraction:**  
   $$
   0.125 = \frac{125}{1000}
   $$
3. **Simplify the Fraction:**  
   GCD of 125 and 1000 is 125.  
   $$
   \frac{125 ÷ 125}{1000 ÷ 125} = \frac{1}{8}
   $$

**Answer:**  
$$
0.125 = \frac{1}{8}
$$

### **2. Converting Decimals to Mixed Numbers**

A mixed number consists of a whole number and a proper fraction.

**Example 4:** Convert 2.5 to a mixed number.

**Steps:**
1. **Separate the Whole Number and Decimal:**  
   - Whole number: 2  
   - Decimal part: 0.5
2. **Convert the Decimal Part to a Fraction:**  
   $$
   0.5 = \frac{5}{10} = \frac{1}{2}
   $$
3. **Combine Them into a Mixed Number:**  
   $$
   2 \frac{1}{2}
   $$

**Answer:**  
$$
2.5 = 2 \frac{1}{2}
$$

---

**Example 5:** Convert 3.75 to a mixed number.

**Steps:**
1. **Separate the Whole Number and Decimal:**  
   - Whole number: 3  
   - Decimal part: 0.75
2. **Convert the Decimal Part to a Fraction:**  
   $$
   0.75 = \frac{75}{100} = \frac{3}{4}
   $$
3. **Combine Them into a Mixed Number:**  
   $$
   3 \frac{3}{4}
   $$

**Answer:**  
$$
3.75 = 3 \frac{3}{4}
$$

---

**Example 6:** Convert 4.2 to a mixed number.

**Steps:**
1. **Separate the Whole Number and Decimal:**  
   - Whole number: 4  
   - Decimal part: 0.2
2. **Convert the Decimal Part to a Fraction:**  
   $$
   0.2 = \frac{2}{10} = \frac{1}{5}
   $$
3. **Combine Them into a Mixed Number:**  
   $$
   4 \frac{1}{5}
   $$

**Answer:**  
$$
4.2 = 4 \frac{1}{5}
$$

### **3. Tips for Simplifying Fractions**

- **Find the Greatest Common Divisor (GCD):** This is the largest number that divides both the numerator and the denominator without leaving a remainder.
  
- **Divide Both Numerator and Denominator by the GCD:**
  $$
  \frac{\text{Numerator}}{\text{Denominator}} = \frac{\text{Numerator ÷ GCD}}{\text{Denominator ÷ GCD}}
  $$
  
- **Ensure the Fraction is in its Simplest Form:** After simplification, the numerator and denominator should have no common divisors other than 1.

### **4. Practice Problems**

Try converting the following decimals to fractions or mixed numbers in simplest form:

1. **0.4**
2. **1.25**
3. **0.333...** (recurring)
4. **5.80**
5. **0.02**

Feel free to attempt these, and if you need solutions or further assistance, let me know!
To convert decimals to fractions or mixed numbers in simplest form: 1. **0.4 = 2/5** 2. **1.25 = 5/4** 3. **0.333... = 1/3** 4. **5.80 = 5 4/5** 5. **0.02 = 1/50** These conversions simplify the decimals to their fraction or mixed number equivalents.

Decimals and Fractions Write each decimal as a fraction or mixed number in simplest fort

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