Convert between decimals and fractions

Key Notes :

🔹 Convert Decimals to Fractions ✅

Step 1: Write the decimal as a fraction with 1 in the denominator.

  • Example: 0.75 → 0.75/1

Step 2: Multiply numerator and denominator to remove the decimal.

  • 0.75/1 × 100/100 = 75/100

Step 3: Simplify the fraction by dividing numerator and denominator by their GCD.

  • 75 ÷ 25 / 100 ÷ 25 = 3/4 ✨

Tip: Repeat decimals → use fraction trick.

  • 0.333… = 1/3 🔄

🔹 Convert Fractions to Decimals 💡

Step 1: Divide numerator by denominator.

  • Example: 7/8 → 7 ÷ 8 = 0.875 🧮

Step 2: If it’s a repeating decimal, show bar notation.

  • 1/3 = 0.333… = 0.\overline{3} 🔁

🔹 Convert Decimals to Mixed Numbers 🔄

Step 1: Separate the whole number from the decimal.

  • Example: 2.75 → 2 + 0.75

Step 2: Convert the decimal part to a fraction.

  • 0.75 → 75/100 → 3/4

Step 3: Combine to make a mixed number.

  • 2 + 3/4 = 2 ¾ 🎯

🔹 Convert Mixed Numbers to Decimals 💫

Step 1: Convert the fraction part to decimal.

  • 2 ¾ → 3 ÷ 4 = 0.75

Step 2: Add the whole number.

  • 2 + 0.75 = 2.75 ✅

🔹 Tips & Tricks 📝

  • Shortcut: Denominators like 2, 4, 5, 8, 10 → easy decimals!
  • Check: Multiply fraction × denominator = numerator? ✔️
  • Use a calculator for tricky repeating decimals 🔢

Learn with an example

Write 1/100  as a decimal number.

Write the fraction as a decimal number with 2 decimal places.

1/100 = 0.01

Write -1/2  as a decimal number.

Start with 1/2,

Write an equivalent fraction with 10 as the denominator. Then write the decimal number.

1/2 = 1 x 5 / 2 x 5

= 5/10

= 0.5

Now write a negative sign on each number:

-1/2 = -0 . 5

Write 11/20  as a decimal number.

Write an equivalent fraction with 100 as the denominator. Then write the decimal number.

11/20 = 11 x 5 / 20 x 5

= 55/100

= 0.55

Let’s practice!🖊️