Decimals, Fractions and Percentages: Connect the Three

A fraction, a decimal and a percentage can name exactly the same amount. Half a whole is 1/2, 0.5 and 50%. Start with that connection before memorising conversion rules. This guide suits learners who can divide whole numbers and recognise simple fractions, typically grades 5–7.

Start with a hundred-square model

Draw a 10 by 10 grid. Shade 25 squares. You shaded 25 out of 100 squares: 25/100. Simplify by dividing the top and bottom by 25 to get 1/4. The decimal is 0.25, and the percentage is 25%. All four expressions describe the same shaded area.

Worked example: turn 3/5 into a decimal and percentage

Divide the numerator by the denominator: 3 ÷ 5 = 0.6. Multiply the decimal by 100 to express it as a percentage: 0.6 × 100 = 60, so the answer is 60%. Check with equivalent fractions: 3/5 = 60/100.

Worked example: a discount in everyday life

A bag costs SAR 80 and has a 15% discount. Convert 15% to 0.15, then calculate 80 × 0.15 = SAR 12. That is the saving. Subtract it from the original price: 80 − 12 = SAR 68. Check: a 10% saving is SAR 8 and a 5% saving is SAR 4; together they make SAR 12.

Three mistakes to catch

• 0.5 is not 5%. It is five tenths, or fifty hundredths: 50%.
• Percent means per hundred. Write 7% as 7/100 = 0.07, not 0.7.
• A discount is the saving. Subtract the saving to find the price you pay.

Try it before checking

• 1. Write 3/4 as a decimal and a percentage.
• 2. Write 0.08 as a percentage and a simplified fraction.
• 3. A SAR 120 item is reduced by 25%. What is the new price?
• 4. Which is larger: 0.4 or 35%? Explain using the same form.

Answers and reasoning

• 1: 3 ÷ 4 = 0.75 = 75%.
• 2: 0.08 = 8% = 8/100 = 2/25.
• 3: 25% of 120 is 30, so the new price is SAR 90.
• 4: 0.4 = 40%, so 0.4 is larger than 35%.

Next step: explain one answer using a shaded grid. If a conversion was difficult, revisit adding and subtracting fractions before choosing a short practice set from the worksheet library.