SI (International System of Units)

A globally agreed system of measurement used in science, based on base units like meter (m), kilogram (kg), second (s), kelvin (K), mole (mol), and ampere (A).

A way of writing numbers as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer, used for very large or very small values.

The digits in a measurement that are known with certainty plus one estimated digit, showing the precision of the measurement.

The variable that is deliberately changed in an experiment to test its effect on another variable.

The variable that is measured in an experiment; it may change when the independent variable changes.

A comparison of two quantities, often expressed as a fraction, such as mass/volume.

Mass per unit volume, often written as density = mass / volume.

What is Direct proportion?

A relationship where one variable changes at a constant rate with another; if one doubles, the other doubles.

Getting Ready for SHS Science: Math, Measurement, and Scientific Thinking — SHS Science Foundations: Integrated Chemistry, Biology, and Physics

Q: Which is the correct scientific notation for 0.00072 m?

7.2 × 10⁻⁴ m. Move the decimal 4 places to the right: 0.00072 → 7.2. Because the original number is less than 1, the exponent is negative. So 0.00072 m = 7.2 × 10⁻⁴ m. Option 2 is wrong because a must be between 1 and 10.

Q: A student tests how the amount of fertilizer affects the mass of tomatoes produced by each plant. What is the dependent variable?

Mass of tomatoes produced by each plant. The dependent variable is what you measure in response to the change. Here, the student changes fertilizer amount (independent variable) and measures the mass of tomatoes (dependent variable). Soil type and water are controlled variables.

Q: Significant figures

The digits in a measurement that are known with certainty plus one estimated digit, showing the precision of the measurement.

Q: Independent variable

The variable that is deliberately changed in an experiment to test its effect on another variable.

Q: Dependent variable

The variable that is measured in an experiment; it may change when the independent variable changes.

Q: What is Ratio?

A comparison of two quantities, often expressed as a fraction, such as mass/volume.

Q: What is Density?

Mass per unit volume, often written as density = mass / volume.

Q: What is Direct proportion?

A relationship where one variable changes at a constant rate with another; if one doubles, the other doubles.

Step 1: Why Math and Measurement Matter in SHS Science

Math as a Science Language

In SHS science, math is the language you use to describe, compare, and predict what happens in experiments. You will not leave math at the door; you will bring it into every lab and problem.

What You Will Refresh

In this module you will review: 1) SI units and scientific notation, 2) significant figures and measurement error, 3) ratios, proportions, and basic algebra, 4) tables and graphs, and 5) the scientific method and experimental design.

Think Like a Scientist

As you learn, picture real lab tasks: reading a ruler, timing a reaction, or plotting data. The goal is to understand how these math tools help you think and work like a scientist, not just to memorize rules.

Step 2: SI Units – The Standard Language of Measurement

What Is SI?

The International System of Units (SI) is the global standard for measurement. Using SI makes your results understandable and comparable anywhere in the world.

Base and Derived Units

Key base units: meter (m) for length, kilogram (kg) for mass, second (s) for time, kelvin (K) for temperature, mole (mol) for amount, ampere (A) for current. From these we build units like m/s for speed and L for volume.

Prefixes You Must Know

Common prefixes: kilo- (k) = 10³, centi- (c) = 10⁻², milli- (m) = 10⁻³, micro- (µ) = 10⁻⁶. For example, 1 km = 1000 m, 1 cm = 0.01 m, 1 mL = 0.001 L.

Everyday SI Examples

A walking speed is about 1.4 m/s, a water bottle might hold 500 mL, and normal body temperature is about 37 °C (310 K). These familiar values help you practice SI thinking.

Step 3: Practice Converting SI Units

Try these quick conversions using the SI prefixes from the previous step. Do them in your head or on paper, then check yourself.

A pencil is 15 cm long. How many meters is that?

Hint: 1 cm = 0.01 m.

A small bottle holds 250 mL of water. How many liters is that?

Hint: 1 mL = 0.001 L.

A runner completes a 5.0 km race. How many meters is that?

Hint: 1 km = 1000 m.

A lab sample has a mass of 0.025 kg. How many grams is that?

Hint: 1 kg = 1000 g.

Suggested answers (do not look until you try):

0.15 m
0.250 L
5000 m
25 g

If any felt tricky, review which direction you moved the decimal point and why.

Step 4: Scientific Notation – Writing Very Big and Very Small Numbers

What Is Scientific Notation?

Scientific notation writes numbers as `a × 10ⁿ` where 1 ≤ a < 10 and n is an integer. It keeps very big or small numbers neat and easy to compare.

Big and Small Examples

Speed of light: 300000000 m/s becomes 3.0 × 10⁸ m/s. Hydrogen atom radius: 0.00000005 m becomes 5.0 × 10⁻⁸ m. The exponent tells you how many decimal places were moved.

Steps to Convert

1) Move the decimal so the first digit is 1–9. 2) Count how many places you moved. 3) Left move gives positive exponent, right move gives negative exponent. Example: 0.00450 s → 4.50 × 10⁻³ s.

Quick Check: Scientific Notation

Test your understanding of scientific notation with this question.

Which is the correct scientific notation for 0.00072 m?

7.2 × 10⁻⁴ m
0.72 × 10⁻³ m
7.2 × 10⁴ m
72 × 10⁻⁵ m

Show Answer

Answer: A) 7.2 × 10⁻⁴ m

Move the decimal 4 places to the right: 0.00072 → 7.2. Because the original number is less than 1, the exponent is negative. So 0.00072 m = 7.2 × 10⁻⁴ m. Option 2 is wrong because a must be between 1 and 10.

Step 5: Significant Figures and Measurement Error

Why Significant Figures?

Every measurement has uncertainty. Significant figures show how many digits in your value are meaningful based on the precision of your instrument, plus one estimated digit.

Counting Sig Figs

Rules: 1) All non-zero digits count. 2) Zeros between non-zeros count. 3) Leading zeros do not count. 4) Trailing zeros after a decimal point do count. Example: 0.0045 has 2 sig figs; 2.300 has 4.

Sig Figs in Calculations

For multiplication/division, match the fewest sig figs. For addition/subtraction, match the fewest decimal places. Example: 2.5 cm × 3.14 cm = 7.85 cm² → 7.9 cm² (2 sig figs).

Step 6: Ratios, Proportions, and Simple Equations in Science

Ratios in Science: Density

Density is a ratio: density = mass / volume. Example: mass 120 g, volume 15.0 cm³ → density = 120 ÷ 15.0 = 8.0 g/cm³. You are comparing how much mass fits in each unit of volume.

Direct Proportion: Distance and Time

With constant speed, distance = speed × time. Example: speed 20 m/s for 15 s → distance = 20 × 15 = 300 m. If time doubles, distance also doubles.

Rearranging Formulas

From distance = speed × time, solving for speed gives speed = distance / time. Example: 150 m in 30 s → speed = 150 ÷ 30 = 5.0 m/s. Steps: choose the variable, isolate it, plug in values with units.

Step 7: Reading Tables and Graphs

Imagine you did an experiment measuring how the temperature of water changes as you heat it. You record time and temperature.

Table A: Heating Water

Time (min) | Temperature (°C)

---------- | ----------------

0 | 22

2 | 35

4 | 48

6 | 61

8 | 74

Now answer these questions (think before checking the hints):

At what time did the water reach about 50 °C?

Hint: Look for the closest temperature in the table.

Between which two times did the temperature increase the most?

Hint: Calculate the change in temperature for each 2-minute interval.

If you plotted this on a graph (time on the x-axis, temperature on the y-axis), would the line slope up or down? What does that tell you?

Hint: Think about whether temperature is increasing or decreasing.

Suggested answers:

Around 4 minutes (48 °C is closest to 50 °C).
All intervals are the same: temperature increases by 13 °C every 2 minutes.
The line would slope upward, showing that as time increases, temperature increases. This is a positive relationship between time and temperature.

Step 8: Scientific Method and Experimental Design Basics

Steps of the Scientific Method

Key steps: 1) Ask a question, 2) Research, 3) Form a hypothesis, 4) Design and run an experiment, 5) Collect and analyze data, 6) Draw conclusions, 7) Communicate results.

Variables in Experiments

Independent variable: what you change. Dependent variable: what you measure. Controlled variables: what you keep the same so they do not confuse your results.

Plant Growth Example

Question: Does light affect plant growth? Independent: hours of light. Dependent: plant height. Controls: plant type, soil, water, temperature, pot size. Only light should be different between groups.

Check Understanding: Variables

Identify the independent and dependent variables in an experiment.

A student tests how the amount of fertilizer affects the mass of tomatoes produced by each plant. What is the dependent variable?

Amount of fertilizer added to each plant
Mass of tomatoes produced by each plant
Type of soil used for each plant
Amount of water given to each plant

Show Answer

Answer: B) Mass of tomatoes produced by each plant

The dependent variable is what you measure in response to the change. Here, the student changes fertilizer amount (independent variable) and measures the mass of tomatoes (dependent variable). Soil type and water are controlled variables.

Step 9: Key Term Review

Flip through these flashcards to review the most important terms from this module.

SI (International System of Units): A globally agreed system of measurement used in science, based on base units like meter (m), kilogram (kg), second (s), kelvin (K), mole (mol), and ampere (A).
Scientific notation: A way of writing numbers as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer, used for very large or very small values.
Significant figures: The digits in a measurement that are known with certainty plus one estimated digit, showing the precision of the measurement.
Independent variable: The variable that is deliberately changed in an experiment to test its effect on another variable.
Dependent variable: The variable that is measured in an experiment; it may change when the independent variable changes.
Controlled variables: Factors kept constant in an experiment so they do not influence the dependent variable.
Ratio: A comparison of two quantities, often written as a fraction, such as density = mass / volume.
Direct proportion: A relationship where one quantity increases or decreases in the same ratio as another (for example, distance is directly proportional to time at constant speed).

Step 10: Put It All Together – Mini Lab Scenario

Imagine this mini lab you might do in SHS:

You drop a small ball from different heights and measure the time it takes to hit the ground. You want to see how height affects fall time.

Identify the variables:

Independent variable = ?
Dependent variable = ?
One controlled variable = ?

You collect this data:

Height (m) | Time (s)

---------- | -------

1.0 | 0.45

1.5 | 0.55

2.0 | 0.64

2.5 | 0.71

Write the height values in scientific notation.
Example: 1.0 m = 1.0 × 10⁰ m.

You calculate an average speed for each height using `speed = distance / time`.

For 2.0 m and 0.64 s, compute speed.
Round to 2 significant figures.