Percentages and Percent Change in Science

Percentages are everywhere in science: a population grows by a percentage, a chemical yields a percentage of product, a measurement changes by a percent from one trial to the next. The single most tested version is percent change — how much something went up or down compared to where it started. One formula handles all of it.

This lesson gives you that formula and shows how to use it for both increases and decreases.

Percent of a Number

First, the basics. To find a percent of a number, turn the percent into a decimal and multiply. \(20\%\) of \(150\) is \[ 0.20 \times 150 = 30. \] To go the other way — what percent one number is of another — divide and multiply by 100. \(30\) out of \(150\) is \[ \dfrac{30}{150} \times 100\% = 20\%. \] These two moves cover most straightforward percent questions.

The Percent Change Formula

Percent change compares a new value to the original value. The formula is \[ \text{percent change} = \dfrac{\text{new}-\text{old}}{\text{old}} \times 100\%. \] If the result is positive, it is an increase; if negative, a decrease. The most common mistake is dividing by the wrong number, so remember: you always divide by the original (old) value.

Example: a plant grows from \(20\) cm to \(26\) cm. The change is \[ \dfrac{26-20}{20} \times 100\% = \dfrac{6}{20} \times 100\% = 30\%. \] The plant’s height increased by \(30\%\).

Increases and Decreases

The same formula handles a drop. Suppose a sample cools and a measurement falls from \(50\) units to \(40\) units: \[ \dfrac{40-50}{50} \times 100\% = \dfrac{-10}{50} \times 100\% = -20\%. \] The negative sign tells you it is a \(20\%\) decrease. On the test, read whether the question asks for an increase or a decrease, and let the sign of your answer confirm it.

Watch: A Short Video Lesson

mathantics walks through this skill clearly in a few minutes. It is a helpful companion to the reading above:

A Routine for Percent Questions

1. Percent of a number: convert the percent to a decimal and multiply.
2. What percent is A of B: compute \(\dfrac{A}{B} \times 100\%\).
3. Percent change: \(\dfrac{\text{new}-\text{old}}{\text{old}} \times 100\%\), always dividing by the original.
4. Positive means increase; negative means decrease.

Practice

1. What is \(25\%\) of \(80\)?
2. \(15\) is what percent of \(60\)?
3. A value rises from \(40\) to \(50\). What is the percent change?
4. A value falls from \(80\) to \(60\). What is the percent change?
5. In the percent change formula, what do you divide by?
6. What does a negative percent change mean?

Answers

1. \(20\).
2. \(25\%\).
3. \(+25\%\) (an increase).
4. \(-25\%\) (a decrease).
5. The original (old) value.
6. The value decreased.

Where This Fits in Your Science Prep

Percentages build on ratios and proportions and pair with mean, median, mode, and range for handling data. See all topics on the Science Topics Hub.