How to Convert Terminating Decimals to Fractions Step-by-Step for Grade 8

📚 Understanding Terminating Decimals

A terminating decimal is a decimal number that has a finite number of digits after the decimal point. In simpler terms, it's a decimal that ends. For example, 0.5, 0.75, and 0.125 are terminating decimals.

📜 History and Background

The concept of decimals evolved from the need for more precise numerical representation than whole numbers could provide. While fractions were used for centuries, decimals offered a more convenient way to perform calculations and express quantities. Terminating decimals, in particular, are closely linked to fractions with denominators that are powers of 10.

📌 Key Principles

• 🔢 Identify the Decimal: Recognize the terminating decimal you want to convert. For example, 0.6.
• 💯 Determine the Place Value: Figure out the place value of the last digit. In 0.6, the 6 is in the tenths place.
• ✍️ Write as a Fraction: Write the decimal as a fraction with the decimal number as the numerator and the place value as the denominator. So, 0.6 becomes $\frac{6}{10}$.
• ➗ Simplify the Fraction: Simplify the fraction to its lowest terms. $\frac{6}{10}$ can be simplified to $\frac{3}{5}$.

💡 Step-by-Step Conversion

1. 🔢 Step 1: Write down the terminating decimal. Let's use 0.45 as an example.
2. 💯 Step 2: Identify the place value of the last digit. In 0.45, the 5 is in the hundredths place.
3. ✍️ Step 3: Write the decimal as a fraction. 0.45 becomes $\frac{45}{100}$.
4. ➗ Step 4: Simplify the fraction. Find the greatest common divisor (GCD) of the numerator and denominator. The GCD of 45 and 100 is 5.
5. ➗ Step 5: Divide both the numerator and the denominator by the GCD. $\frac{45 \div 5}{100 \div 5} = \frac{9}{20}$.
6. ✅ Step 6: The simplified fraction is $\frac{9}{20}$. Therefore, 0.45 is equal to $\frac{9}{20}$.

➕ More Examples

• Example 1: Convert 0.75 to a fraction.
  • 0. 75 = $\frac{75}{100}$
  • Simplify: $\frac{75 \div 25}{100 \div 25} = \frac{3}{4}$
  • So, 0.75 = $\frac{3}{4}$
• Example 2: Convert 0.125 to a fraction.
  • 0. 125 = $\frac{125}{1000}$
  • Simplify: $\frac{125 \div 125}{1000 \div 125} = \frac{1}{8}$
  • So, 0.125 = $\frac{1}{8}$
• Example 3: Convert 1.2 to a fraction.
  • 1. 2 = $\frac{12}{10}$
  • Simplify: $\frac{12 \div 2}{10 \div 2} = \frac{6}{5}$
  • So, 1.2 = $\frac{6}{5}$

🌍 Real-World Examples

• 📏 Measurements: Converting decimal measurements (like 0.5 inches) to fractions ($\frac{1}{2}$ inch) for easier understanding in construction or crafting.
• 🍕 Sharing: Dividing a pizza into equal slices. If you have 0.25 of the pizza, that's $\frac{1}{4}$ of the pizza.
• 💰 Finance: Calculating discounts. If an item is 0.20 off, that's $\frac{1}{5}$ off the original price.

📝 Practice Quiz

Convert the following terminating decimals to fractions in their simplest form:

1. 0.2
2. 0.65
3. 0.8
4. 0.375
5. 0.9

Answers:

1. $\frac{1}{5}$
2. $\frac{13}{20}$
3. $\frac{4}{5}$
4. $\frac{3}{8}$
5. $\frac{9}{10}$

✅ Conclusion

Converting terminating decimals to fractions is a fundamental skill in mathematics. By understanding the place value system and simplifying fractions, you can easily convert any terminating decimal into its fractional form. This skill is useful in various real-world applications, making it an essential concept to master. Keep practicing, and you'll become a pro in no time!