← ACARA Digital Technologies Years 7–8

Calculating percentage change

Percentage change: (new - old) / old, formatted as a percentage. A positive result is a rise, a negative result is a fall. Use it for year-on-year growth.

Part of: ACARA Digital Technologies Years 7–8 — Analysing and Visualising Data — Module 31, ACARA Digital Technologies Years 9–10 — Analysing and Visualising Data — Module 28

Understanding Calculating percentage change in ACARA Digital Technologies Years 7–8

What it does: Year-on-year growth compares this year (new) with last year (old), so you work out (new - old) / old. After dividing the difference by the old value, applying the Percentage format turns a decimal such as 0.2 into 20%. (250-200)/200 = 50/200 = 0.25, which is 25%. Dividing by the new value (250) would wrongly give 20%. A negative result means the new value is lower than the old value, so it is a fall. (50-50)/50 = 0/50 = 0. No difference means 0% change. The formula subtracts old from new, then divides by old, which gives the change as a fraction of where you started.

Common mistakes: Percentage change divides by the OLD value (B2), not the new value. The formula should be =(C2-B2)/B2. The subtraction is the wrong way round (old - new). It must be new - old, so a rise gives a positive result: =(C2-B2)/B2.

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This module's key terms are also in a printable crossword (Modules 302–324) and word search (Modules 261–324).

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Learning
Duo
Which formula calculates the percentage change from an old value in B2 to a new value in C2?
=(C2-B2)/C2=(C2-B2)/B2
Matches
=C2-B2/B2
↓
Missing brackets, so B2/B2 is worked out first (giving 1) and then subtracted from C2. It should be =(C2-B2)/B2.
Applying
Meanings
Term
=(C2-B2)/B2
Meaning
Percentage change: (new - old) / old, formatted as a percentage. A positive result is a rise, a negative result is a fall. Use it for year-on-year growth.
Practice
=ROUND((D2-B2)/B2,3)
Testing
Gaps
=(C2-B2)/
Check Answer
Spots
3C2: 60 (new price)
4D2: =(C2-B2)/C2

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Quick Questions

1. Which formula calculates the percentage change from an old value in B2 to a new value in C2?
A. =(C2-B2)/C2
B. =(C2-B2)/B2 ✓
Percentage change divides the difference by the OLD value (B2), because you are measuring change from where you started.
2. A shop's sales go from 200 to 250. What is the percentage change?
A. +20% (a rise)
B. +25% (a rise) ✓
(250-200)/200 = 50/200 = 0.25, which is 25%. Dividing by the new value (250) would wrongly give 20%.
3. A cell shows -0.15 formatted as a percentage. What does this tell you?
A. The value fell by 15% ✓
B. The value rose by 15%
A negative result means the new value is lower than the old value, so it is a fall.
4. In year-on-year growth, which value is the 'old' value in the formula?
A. Last year's value ✓
B. This year's value
Year-on-year growth compares this year (new) with last year (old), and the old value goes under the division.
5. Your formula =(C2-B2)/B2 shows 0.12 in the cell. What should you do to show it as a percentage?
A. Format the cell as a percentage to show 12% ✓
B. Multiply the formula by 12 to show 12%
The result 0.12 is already correct. Applying Percentage format displays it as 12%, with no extra maths needed.

Match the Pairs

=(C2-B2)/B2 → Percentage change from the old value in B2 to the new value in C2, shown as a decimal until formatted as a percentage
=(C2-B2)/B2 giving -0.15 → A fall of 15% from the old value to the new value
Year-on-year growth: last year's sales are in B2 and this year's sales are in C2 → =(C2-B2)/B2
Percentage change is found by dividing the change by the old value, with the result formatted as a percentage → =(C2-B2)/B2 with Percentage format
=C2-B2/B2 → Missing brackets, so B2/B2 is worked out first (giving 1) and then subtracted from C2. It should be =(C2-B2)/B2.
=(C2-B2)/C2 → Divides by the new value instead of the old value. It should be =(C2-B2)/B2.

Key Term

=(C2-B2)/B2
Percentage change: (new - old) / old, formatted as a percentage. A positive result is a rise, a negative result is a fall. Use it for year-on-year growth.

Fill in the Blanks

1. =(C2-B2)/B2
Hint: Type the cell reference of the old value, which you divide the change by.
2. =(C2-B2)/B2
Hint: Type the operator that finds the change by taking the old value away from the new value.
3. =(C2-B2)/B2
Hint: Type the operator that turns the change into a fraction of the old value.
4. =(C2-B2)/B2
Hint: Type the cell reference of the new value, the more recent year.
5. =(D2-C2)/C2
Hint: This is year-on-year growth from the second year to the third. Type the cell for the previous year, which is the old value.

Spot the Error

Question 1
A A2: Shoes
B B2: 50 (old price)
C C2: 60 (new price)
D D2: =(C2-B2)/C2
E Format D2 as Percentage
Line D — Percentage change divides by the OLD value (B2), not the new value. The formula should be =(C2-B2)/B2.
Question 2
A B2: 200 (old)
B C2: 250 (new)
C D2: =(B2-C2)/B2
D Format D2 as Percentage
Line C — The subtraction is the wrong way round (old - new). It must be new - old, so a rise gives a positive result: =(C2-B2)/B2.
Question 3
A D2: =C2-B2/B2
B D2 result: 0.25
C Format D2 as Percentage
Line A — Without brackets, B2/B2 is worked out first, so the formula gives C2-1. The subtraction needs brackets: =(C2-B2)/B2.
Question 4
A (C3-B3)/B3
B B3 = 80, C3 = 60
C Result: -0.25 (-25%)
D A fall of 25%
Line A — Every spreadsheet formula must start with =. Without it the cell just shows text. It should be =(C3-B3)/B3.
Question 5
A Old in B2, new in C2
B D2: =(C2-B2)/B2*100
C Format D2 as Percentage
Line B — Multiplying by 100 is not needed because the Percentage format already does that. It would show 2500% instead of 25%. Use =(C2-B2)/B2.

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