Percentages and Decimals: A Comprehensive Guide for GCSE Students

This page provides a detailed explanation of how to convert percentages to decimals and calculate percentages of numbers, which is crucial for GCSE mathematics. The content is particularly useful for students preparing for GCSE foundation percentage problems.

The guide begins by presenting common percentage-to-decimal conversions:

• 50% = 1/2 = divide by 2
• 25% = 1/4 = divide by 4
• 75% = 3/4
• 20% = 1/5 = divide by 5

These conversions serve as a quick reference for students to memorize and apply in various mathematical problems.

Example: A foundation GCSE exam question asks students to write 45% as a decimal. The correct answer is 0.45.

The guide then delves into more complex percentage calculations with two detailed examples:

1. Finding 27% of 50:

   • Step 1: Convert the percentage to a decimal by dividing by 100 (27/100 = 0.27)
   • Step 2: Multiply the decimal by the number (0.27 × 50 = 13.5)
   • The final answer is 13.5

2. Finding 17% of 160m:

   • Step 1: Convert 17% to a decimal (17/100 = 0.17)
   • Step 2: Multiply the decimal by 160 (0.17 × 160 = 27.2)
   • Step 3: Check and include the units of measure
   • The final answer is 27.2m

Highlight: It's crucial to pay attention to units of measure when solving percentage problems, especially in real-world applications.

These examples demonstrate the step-by-step process of how to calculate percentage of a number, which is a fundamental skill for GCSE mathematics and beyond.

Vocabulary: Decimal - A number expressed in the scale of tens, particularly such a number expressed as a decimal fraction.

Definition: Percentage - A number or ratio expressed as a fraction of 100.

This comprehensive guide equips students with the necessary knowledge and techniques to confidently approach percentage problems in their GCSE exams and everyday life situations involving percentages and decimals.