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Percentages – Large and Small

📘 Notes

Percentages Less Than 1% and Greater Than 100% (Year 7)

Percentages can be very small (less than 1%) or very large (more than 100%).

1. Percentages Less Than 1%

If a percentage is less than 1%, it is less than 1 part out of 100.

\[ 1\% = \frac{1}{100} \quad\Rightarrow\quad 0.5\% = \frac{0.5}{100} = \frac{1}{200} \]

Examples:

  • 0.5% of 200 students = \(0.005 \times 200 = 1\)
  • 0.2% of 500g = \(0.002 \times 500 = 1\text{g}\)
  • 0.1% of 1000 = \(0.001 \times 1000 = 1\)

Tip: Always change small percentages to decimals.

\[ 0.5\% = 0.005,\qquad 0.2\% = 0.002,\qquad 0.1\% = 0.001 \]

2. Percentages Greater Than 100%

A percentage greater than 100% is more than the whole amount.

Examples:

  • 120% means more than 100%
  • 150% means one and a half times
  • 200% means twice
\[ 150\% = 1.5,\qquad 200\% = 2,\qquad 250\% = 2.5 \]

Example:

120% of 40 students = \(1.2 \times 40 = 48\)

200% of 12kg = \(2 \times 12 = 24\text{kg}\)

3. Comparing Percentages

Smaller than 1%: very small amounts (tiny percentages).

Greater than 100%: more than the whole amount.

Percentage Decimal Meaning
0.5%0.005Very small
100%1Whole amount
150%1.5One & a half times
200%2Twice the amount

4. Try These

Find the values:

  1. 0.2% of 500g
  2. 150% of 24cm
  3. 0.1% of 2000
  4. 125% of 80kg
  5. 0.05% of 500

Give your answers with correct units.