← Years 9–10 Data & Information

Calculating compression ratio and space saved

Original size divided by compressed size. Percentage saved = (original - compressed) / original x 100. Example: 10 MB down to 2 MB is a ratio of 5 to 1, saving 80%.

Part of: 9-10 Digital Technologies: Data compression — Module 16, ACARA Digital Technologies Years 9–10 — Data Compression — Module 38

Understanding Calculating compression ratio and space saved in Years 9–10 Data & Information

What it does: Original size (10 MB) divided by compressed size (2 MB) gives a ratio of 5, written as 5 to 1. (50 - 10) / 50 x 100 = 80%. The 20% is the share of the file that is left, not the amount saved. Percentage saved is always measured against the original size, so divide by the original. 200 / 50 = 4, so the ratio is 4 to 1. Saved: (200 - 50) / 200 x 100 = 75%. 8 / 8 = 1, so the ratio is 1 to 1. Saved: (8 - 8) / 8 x 100 = 0%. Nothing was saved.

Common mistakes: Percentage saved is divided by the ORIGINAL size, not the compressed size. It should be pct ← diff / orig * 100, which gives 80. Compression ratio is original size divided by compressed size. It should be ratio ← 10 / 2, which gives 5 (a ratio of 5 to 1).

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Learning
Duo
A 10 MB video is compressed to 2 MB. What is the compression ratio?
2 to 1 (compressed / original)5 to 1 (10 / 2)
Matches
ratio = compressed / original
↓
The sizes are the wrong way around. The ratio should be original divided by compressed, so 10 MB down to 2 MB gives 5, not 0.2.
Applying
Meanings
Term
compression ratio = original size / compressed size
Meaning
Original size divided by compressed size. Percentage saved = (original - compressed) / original x 100. Example: 10 MB down to 2 MB is a ratio of 5 to 1, saving 80%.
Practice
original ← 10
Testing
Gaps
ratio ← original /
Check Answer
Spots
3diff ← orig - comp
4pct ← diff / comp * 100

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Quick Questions

1. A 10 MB video is compressed to 2 MB. What is the compression ratio?
A. 5 to 1 (10 / 2) ✓
B. 2 to 1 (compressed / original)
Compression ratio = original size / compressed size. 10 / 2 = 5, so the ratio is 5 to 1.
2. Which formula gives the compression ratio?
A. compressed size / original size
B. original size / compressed size ✓
The ratio puts the original size on top and the compressed size underneath. A bigger ratio means more compression.
3. A 50 KB file is compressed to 10 KB. What percentage of space was saved?
A. 20%
B. 80% ✓
(50 - 10) / 50 x 100 = 80%. The 20% is the share of the file that is left, not the amount saved.
4. Which formula gives the percentage saved?
A. (original - compressed) / original x 100 ✓
B. (original - compressed) / compressed x 100
Percentage saved is always measured against the original size, so divide by the original.
5. A 200 MB file is compressed to 50 MB. Which statement is correct?
A. The ratio is 4 to 1 and 75% was saved ✓
B. The ratio is 4 to 1 and 25% was saved
200 / 50 = 4, so the ratio is 4 to 1. Saved: (200 - 50) / 200 x 100 = 75%.

Match the Pairs

ratio = original / compressed → Works out the compression ratio by dividing the original size by the compressed size
saved = (original - compressed) / original * 100 → Works out the percentage of space saved by compression
A 10 MB file compressed to 2 MB has a compression ratio of 5 to 1 → 10 / 2 = 5
Technique A shrinks 50 MB to 10 MB and technique B shrinks 50 MB to 25 MB, so A saves more space → (50 - 10) / 50 * 100 = 80 and (50 - 25) / 50 * 100 = 50
ratio = compressed / original → The sizes are the wrong way around. The ratio should be original divided by compressed, so 10 MB down to 2 MB gives 5, not 0.2.
saved = (10 - 2) / 2 * 100 → The percentage saved is divided by the compressed size (2). It must be divided by the original size (10), giving 80%, not 400%.

Key Term

compression ratio = original size / compressed size
Original size divided by compressed size. Percentage saved = (original - compressed) / original x 100. Example: 10 MB down to 2 MB is a ratio of 5 to 1, saving 80%.

Fill in the Blanks

1. ratio ← original / compressed
Hint: Type the variable for the file size after compression, which the ratio is divided by.
2. saved ← (original - compressed) / original percent ← saved * 100
Hint: Type the variable that the space saved is divided by to get a fraction.
3. original ← 10 compressed ← 2 saved ← (original - compressed) / original
Hint: Type the operator that works out how much space was removed.
4. saved ← 8 / 10 percent ← saved * 100
Hint: Type the number you multiply by to turn a fraction into a percentage.
5. ratioA ← 12 / 4 ratioB ← 12 / 3 IF ratioA < ratioB THEN OUTPUT "B"
Hint: Type the comparison operator that checks whether A has a smaller ratio than B, so B compresses better.

Spot the Error

Question 1
A orig ← 10
B comp ← 2
C diff ← orig - comp
D pct ← diff / comp * 100
Line D — Percentage saved is divided by the ORIGINAL size, not the compressed size. It should be pct ← diff / orig * 100, which gives 80.
Question 2
A ratio ← 2 / 10
B pct ← (10 - 2) / 10 * 100
C DISPLAY ratio, pct
Line A — Compression ratio is original size divided by compressed size. It should be ratio ← 10 / 2, which gives 5 (a ratio of 5 to 1).
Question 3
A orig ← 50
B comp ← 10
C saved ← orig + comp
D pct ← saved / orig * 100
Line C — The space saved is the original size MINUS the compressed size, not plus. It should be saved ← orig - comp, which gives 40.
Question 4
A ratioA ← 60 / 20
B ratioB ← 30 / 60
C IF ratioA > ratioB THEN
D DISPLAY 'A is better'
Line B — Both ratios must be original divided by compressed. Technique B should be ratioB ← 60 / 30 (a ratio of 2), so it can be compared fairly with A (a ratio of 3).
Question 5
A ratio ← 10 / 2
B saved ← 10 - 2
C pct ← saved / 10
D DISPLAY pct
Line C — The division gives a fraction (0.8). It must be multiplied by 100 to become a percentage. It should be pct ← saved / 10 * 100, which gives 80.

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