Convert between decimals and fractions

Key Notes :

1. Understanding the Relationship Between Decimals and Fractions

• Decimals and fractions are two different ways of representing parts of a whole.
• Both can be used interchangeably to express numbers that are less than 1, greater than 1, or equal to a whole number.

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2. Converting Decimals to Fractions

• Step 1: Write the decimal number over a power of 10 (e.g., 0.5 becomes 5/10).
  • The number of decimal places determines the denominator:
    • 1 decimal place → denominator is 10.
    • 2 decimal places → denominator is 100.
    • 3 decimal places → denominator is 1,000, etc.
• Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF).
  • Example:
    • Convert 0.75 to a fraction:
      0.75 = 75/100 → simplify by dividing by 25 → 3/4.

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3. Converting Fractions to Decimals

• Step 1: Divide the numerator by the denominator using long division.
• Step 2: If the division ends with a remainder of zero, the decimal is terminating.
• Step 3: If the division repeats, it’s a repeating decimal.
  • Example:
    • Convert 1/4 to a decimal:
      1 ÷ 4 = 0.25 (terminating decimal).
    • Convert 1/3 to a decimal:
      1 ÷ 3 = 0.333… (repeating decimal, often written as 0.\overline{3}).

Learn with an example

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