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Observations and Measurement

Every idea in this book rests on the same three things. You need careful observation, honest measurement, and a clear sense of the difference between what you saw and what you concluded from it. This chapter builds those skills, from density to reading graphs, and the Regents uses them everywhere.

About 18 minutes · Formulas to know by heart: density, percent deviation, rate of change

  1. Observations and inferences01
  2. Measurement02
  3. Density03
  4. Interactive: density lab04
  5. Percent deviation05
  6. Graphs and rates06
  7. The short version07
01

Observations and inferences

Science starts with observation. An observation is information you gather directly with your senses, or with instruments that extend your senses. "The rock is gray, feels rough, and has a mass of 340 grams" is a set of observations. An inference is different. It is a conclusion you draw from observations. "This rock formed from cooling lava" is an inference, because nobody watched it happen.

The whole course depends on this difference. Earth scientists rarely get to watch mountains rise or ice ages come and go. So nearly everything we know about Earth's past is inference, built carefully on top of observations we can make today. Good science keeps the two separate. State what you actually observed, then explain what you think it means. Classification means grouping things by their observed properties, and it is how observations get organized into something useful.

Here is a quick test. Could a measuring tool or one of your senses record it directly? If yes, it is an observation. If it took interpretation to get there, it is an inference.

Watch: Observations and Inferences, the foundation skill for everything in this course. Video by Mike Sammartano.
02

Measurement

A measurement is an observation with a number and a unit attached. Earth science uses the metric system. Mass is measured in grams with a balance. Volume is measured in milliliters or cubic centimeters, either with a graduated cylinder or by calculating it from the object's dimensions. Length is measured in meters and temperature in degrees Celsius. One milliliter equals one cubic centimeter, which makes it easy to compare liquid and solid volumes.

To find the volume of an irregular object such as a rock, use water displacement. Put the rock under water and the rise in the water level equals its volume. Every measurement carries some uncertainty, because instruments and the people reading them are not perfect. That is not a failure. It is the reason scientists report how they measured something and check each other's numbers.

Watch: Measuring and Calculating Volume. Video by Mike Sammartano.
03

Density

Density is how tightly matter is packed. It is the mass of a substance per unit of volume. The formula is density equals mass divided by volume, with units like grams per cubic centimeter. Learn it. Unlike the older Earth Science tables, the 2026 Reference Tables do not print the equations, so these formulas have to be in your head. Water has a density of 1.0 g/mL, which makes it a useful comparison. Anything denser than water sinks in it, and anything less dense floats.

Here is the idea students miss most often. Density is a property of the substance, not of the sample. Cut a brick in half and each piece has half the mass and half the volume, so the density does not change. Size does not matter. Squeezing and heating do change density. Compression packs the same mass into less space, which raises density. Heating makes most materials expand, which lowers it. That is why cold air sinks and warm air rises, an idea the weather unit depends on later.

Water is the famous exception. As it freezes it expands, so ice is less dense than liquid water and floats. Water is densest as a liquid at 3.98 degrees Celsius, a number the Regents rounds to an even 4.

D < 1: floats D ≈ 1: hangs D > 1: sinks water, density 1.0 g/mL
Figure 1.1.1 · Density against water. Less than 1.0 g/mL floats, about 1.0 hovers, more than 1.0 sinks. The size of the block never matters, only the substance.
An iceberg floating in calm Arctic water with most of its mass visible below the surface, only a small portion rising above the waterline.
Figure 1.1.2 · An iceberg is density made visible: ice at about 0.9 g/mL floats in seawater at about 1.03 g/mL, with roughly nine tenths of it hidden below the surface. AWeith, via Wikimedia Commons (CC BY-SA 4.0).
04

Density lab

Set a mass and a volume and the lab computes the density from the formula, then tells you whether the sample would sink or float in water. Try doubling both mass and volume together and watch the density hold still.

Mass: 120 g
Volume: 100 mL
05

Percent deviation

How far off is a measurement? Percent deviation compares your value to the accepted value. Take the difference between them, divide by the accepted value, then multiply by 100. Say the accepted density of quartz is 2.7 g/cm³ and you measured 3.0. Your deviation is 0.3 divided by 2.7, which is about 11 percent.

Notice that the accepted value always goes on the bottom. The same size error matters more when the true value is small, and percent deviation captures that.

Watch: Rounding Measurements. Video by Mike Sammartano.
06

Rates of change and graphs

Earth is always changing, and rate of change measures how fast. It is the change in a value divided by the time it took. A stream that rises 6 centimeters in 3 hours is rising at 2 centimeters per hour. This formula shows up everywhere, from cooling magma to moving plates.

Graphs let you see relationships. In a direct relationship both variables rise together, so the line slopes up. In an inverse relationship one rises as the other falls, so the line slopes down. Many of Earth's changes are cyclic, which means they repeat in a regular pattern. The seasons, the tides, and the phases of the moon all do this, and they trace a wave on a graph. Recognizing these three shapes quickly is a Regents skill worth practicing.

direct inverse cyclic
Figure 1.1.3 · The three graph shapes to know on sight: direct (up together), inverse (one up, one down), and cyclic (a repeating pattern over time).
07

The short version

Observations come from your senses and from instruments. Inferences are the conclusions you build on top of them, and Earth science is mostly careful inference about a past nobody watched. Measurements attach numbers and metric units to observations. Density is mass divided by volume. It is a property of the substance and does not depend on sample size. Water sits at 1.0 g/mL, which is the line between floating and sinking, and ice is the famous exception that floats. Percent deviation measures how far a measurement misses the accepted value. Rate of change measures how fast something happens. Graphs come in three shapes worth knowing cold, which are direct, inverse, and cyclic.

08

Practice

On the Regents exam

Measurement shows up as density calculations and as observation-versus-inference multiple choice. Expect at least one percent-deviation or rate-of-change problem. Because the 2026 Reference Tables no longer print the equations, memorize density, percent deviation, and rate of change.

Worked example: Find the density of a rock

A rock has a mass of 45 g and a volume of 15 cm³. What is its density, and will it float in water?

  1. Recall the equation: density = mass ÷ volume.
  2. Substitute: 45 g ÷ 15 cm³.
  3. Divide: 3.0 g/cm³.
  4. Compare to water (1.0 g/cm³). Since 3.0 is greater, the rock sinks.

Answer: 3.0 g/cm³, and it sinks.

Ten Regents-style questions, one at a time in a focused view, each with an instant explanation. The set reshuffles when you reach the end, so you can keep practicing as long as you like.

Unit 1 checkpoint

You have finished Measurement. Try a focused quiz on just this unit before moving on, with instant explanations and a topic breakdown.

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