1.3: Metric Measurements

Last updated
Save as PDF

Page ID: 222585

Sharbani Banerjee, Casey Barr, Joe Frantz, Melissa Graham, Tyler Wilson
Oxnard College

$ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $

$ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} $

$ \newcommand{\dsum}{\displaystyle\sum\limits} $

$ \newcommand{\dint}{\displaystyle\int\limits} $

$ \newcommand{\dlim}{\displaystyle\lim\limits} $

$ \newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$

( \newcommand{\kernel}{\mathrm{null}\,}\) $ \newcommand{\range}{\mathrm{range}\,}$

$ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$

$ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$

$ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$

$ \newcommand{\Span}{\mathrm{span}}$

$ \newcommand{\id}{\mathrm{id}}$

$ \newcommand{\Span}{\mathrm{span}}$

$ \newcommand{\kernel}{\mathrm{null}\,}$

$ \newcommand{\range}{\mathrm{range}\,}$

$ \newcommand{\RealPart}{\mathrm{Re}}$

$ \newcommand{\ImaginaryPart}{\mathrm{Im}}$

$ \newcommand{\Argument}{\mathrm{Arg}}$

$ \newcommand{\norm}[1]{\| #1 \|}$

$ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$

$ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\AA}{\unicode[.8,0]{x212B}}$

$ \newcommand{\vectorA}[1]{\vec{#1}} % arrow$

$ \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$

$ \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $

$ \newcommand{\vectorC}[1]{\textbf{#1}} $

$ \newcommand{\vectorD}[1]{\overrightarrow{#1}} $

$ \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} $

$ \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} $

$ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $

$\newcommand{\longvect}{\overrightarrow}$

$ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} $

$\newcommand{\ket}[1]{\left| #1 \right>}$
$\newcommand{\bra}[1]{\left< #1 \right|}$
$\newcommand{\braket}[2]{\left< #1 \vphantom{#2} \right| \left. #2 \vphantom{#1} \right>}$
$\newcommand{\braopket}[3]{\left< #1 \vphantom{#2}\vphantom{#3} \right| #2 \vphantom{#1}\vphantom{#3} \left| #3 \vphantom{#1}\vphantom{#2} \right>}$
$\newcommand{\qmvec}[1]{\mathbf{\vec{#1}}}$
$\newcommand{\op}[1]{\hat{\mathbf{#1}}}$
$\newcommand{\expect}[1]{\langle #1 \rangle}$
$\newcommand{\dfn}[1]{\emph{\textbf{#1}}}$

$\newcommand{\avec}{\mathbf a}$ $\newcommand{\bvec}{\mathbf b}$ $\newcommand{\cvec}{\mathbf c}$ $\newcommand{\dvec}{\mathbf d}$ $\newcommand{\dtil}{\widetilde{\mathbf d}}$ $\newcommand{\evec}{\mathbf e}$ $\newcommand{\fvec}{\mathbf f}$ $\newcommand{\nvec}{\mathbf n}$ $\newcommand{\pvec}{\mathbf p}$ $\newcommand{\qvec}{\mathbf q}$ $\newcommand{\svec}{\mathbf s}$ $\newcommand{\tvec}{\mathbf t}$ $\newcommand{\uvec}{\mathbf u}$ $\newcommand{\vvec}{\mathbf v}$ $\newcommand{\wvec}{\mathbf w}$ $\newcommand{\xvec}{\mathbf x}$ $\newcommand{\yvec}{\mathbf y}$ $\newcommand{\zvec}{\mathbf z}$ $\newcommand{\rvec}{\mathbf r}$ $\newcommand{\mvec}{\mathbf m}$ $\newcommand{\zerovec}{\mathbf 0}$ $\newcommand{\onevec}{\mathbf 1}$ $\newcommand{\real}{\mathbb R}$ $\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$ $\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$ $\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$ $\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$ $\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$ $\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$ $\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$ $\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$ $\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$ $\newcommand{\laspan}[1]{\text{Span}\{#1\}}$ $\newcommand{\bcal}{\cal B}$ $\newcommand{\ccal}{\cal C}$ $\newcommand{\scal}{\cal S}$ $\newcommand{\wcal}{\cal W}$ $\newcommand{\ecal}{\cal E}$ $\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$ $\newcommand{\gray}[1]{\color{gray}{#1}}$ $\newcommand{\lgray}[1]{\color{lightgray}{#1}}$ $\newcommand{\rank}{\operatorname{rank}}$ $\newcommand{\row}{\text{Row}}$ $\newcommand{\col}{\text{Col}}$ $\renewcommand{\row}{\text{Row}}$ $\newcommand{\nul}{\text{Nul}}$ $\newcommand{\var}{\text{Var}}$ $\newcommand{\corr}{\text{corr}}$ $\newcommand{\len}[1]{\left|#1\right|}$ $\newcommand{\bbar}{\overline{\bvec}}$ $\newcommand{\bhat}{\widehat{\bvec}}$ $\newcommand{\bperp}{\bvec^\perp}$ $\newcommand{\xhat}{\widehat{\xvec}}$ $\newcommand{\vhat}{\widehat{\vvec}}$ $\newcommand{\uhat}{\widehat{\uvec}}$ $\newcommand{\what}{\widehat{\wvec}}$ $\newcommand{\Sighat}{\widehat{\Sigma}}$ $\newcommand{\lt}{<}$ $\newcommand{\gt}{>}$ $\newcommand{\amp}{&}$ $\definecolor{fillinmathshade}{gray}{0.9}$

How We Measure in Science

Learning Objectives

2.1 Metric System of Measurements and the base 10
- Convert from one unit magnitude to another
2.2 Measuring Lengths
- Determine which units to use
- Practice measuring different lengths with different tools
2.3 Mass and Weight
- Define mass
  - Understand why we use weight to find mass
- Define weight
2.4 Volume and Density
- Ways to measure volume
- Define density
  - Be able to calculate/measure density
2.5 Temperature
- Compare and contrast Fahrenheit and Celsius
  - Where might Fahrenheit be more appropriate in science
- Understand the defining events for setting the scale of Celsius
- Convert from Fahrenheit to Celsius and back

Introduction

Scientists needed a uniform set of units for which to measure with, leading to the creation of the Metric System. One of the major innovations of the metric system was to create units all related on a base 10 scale. Making it easy to convert 50 cm to .5 meters, or 30 cm³ to .03 L. Making a standardized system of measurements made it easier for scientists to communicate, increasing science’s ability to build on new discoveries.

Table 1 Metric conversions

Distance

.001

Kilometer (km)

1 Meters (m)

100

Centimeters (cm)

1000

Millimeters (mm)

10 (10⁶)

Micrometer (µm)

10(0⁹)

Nanometer (nm)

Volume

.001 Kiloliter (kl)

1 Liter (L)

100 Centiliters (cl)

1000 Milliters (ml)

10 (10⁶)

Microliter (µl)

10(0^₉) Nanoliter (nl)

Mass

.001

Kilogram (kg)

1 Gram (g)

100

Centigrams (cg)

1000

Milligrams (mg)

10 (10⁶)

Microgram (µg)

10(0⁹) Nanogram (ng)

Weight

.001

Kilonewtons (kn)

Newton (N)

100

Centinewton (cn)

1000

Millinewton (mn)

10 (10⁶)

Micronewton (µn)

10(0⁹)

Nanonewton (nn)

Experimental procedure measuring length and conversions

Using small ruler measure some objects to the nearest mm, then convert them as directed.

Small wooden dowel is mm long and cm long and m long.
Small pebble (you can use calipers for this one, calipers can be helpful for measuring oddly shaped objects consistently) is mm long and µm long and nm long.
The metric system also makes it easy to convert from cm³ to ml when measuring volume, as 1 cm³ is equal to 1 ml. Get one of the small wooden blocks and measure its length, width, and height with a small ruler in mm. Then multiply all three of those numbers together to get the volume in mm³ after that convert to cm³ then finally to ml.
Get one of the large meter sticks and measure one of the provided bones cm and convert it to m and then finally to mm.

Mass and Weight

Mass is the measure of how much matter is present in object either living or not. It is fundamentally different than weight, which is the measure of how much force an object exerts on another object based on their gravitational attraction. On Earth we frequently these terms interchangeably, this is because the Earth pulls on all objects on or near its surface equally. In other countries where it is common to use the metric system when asked how much they weigh, the normal response is in kg the unit of mass. The easiest way to see the difference between these is if someone is 75 kg on Earth, they would still be 75 kg on Mars (a planet with a smaller gravitational pull). However someone who is 165 pounds on Earth would only weigh 62.2 pounds.

We use this interchangeably on Earth also because we calculate an objects mass with scales that measure an objects weight. This is due to any object on Earth that weighs 165.35 pounds will always be an object with 75 kg of mass.

Experimental procedure Mass

Using a scale measure the mass of several objects and record the results in the table below.
Then convert all of the mass to mg.

pebbles, wooden dowel, and wooden block — Figure 1: Possible objects to be weighed, from left to right: Pebbles, wooden dowels, and wooden block. The dowels and the block are geometric shapes with calculable surface areas and volumes if their dimensions are measured. The pebbles represent objects with non-calculable surface areas or volumes.

Table 2 Masses

Object	Pebble	Wooden dowel	Wooden block	Glass ball	Copper ball
Mass in (g)
Mass in (mg)

Follow-up questions

What units would you use to measure a person’s mass?
What units would you use to measure a person’s height?
What units would you use to measure the diameter of a cell?
What units would you use to measure the volume of femur bone?
Why wouldn’t you use µm to measure a person’s height?

Volume and Density

Volume is the measure of how much three dimensional space an object takes up. For basic rectangular object you can simply multiply an objects width X height X length to get its volume. In the metric system we can use both cubed measurements of distance such as cm³ as well as conversions of liters. Switching between the two is also easily done as 1 cm³ is the same as 1 ml. Cylinders and spheres are also easily measured for their volume using the formulas

V= $π$ r² h and V= $π$ r³

where $π$ is 3.14, r is the radius of the cylinder or sphere, and h is the height of the cylinder.

For odd shaped objects it can difficult to measure their volume, instead we can use their displacement to calculate their volume. A graduated cylinder is a glass tube that has been graduated with measurements of volume, usually ml or l. When filled with water of a certain amount for example 50ml in a 100ml graduated cylinder, if we then drop an object such as a pebble into the water, then the displacement of the water in ml will be equal to the volume of the pebble.

Experimental procedure measuring and calculating volume

Using the same objects that we measured for mass, measure and calculate their volume. You should make sure to choose the appropriate method for finding their volume. Fill out the table of volumes below.

Table 3 Volumes

Object	Pebble	Wooden dowel	Wooden block	Glass ball	Copper ball
Volume in (cm³)
Volume in (ml)

Figure 2: Example of a graduated cylinder for measuring liquid volume. Always measure at the bottom of the meniscus. Due to surface tension created by Hydrogen bonds in water, the surface of the water will form a depression rather than being flat.

Now that we have found the mass and the density of several objects we can also find their densities. Density is the relationship between the mass of an object and its volume. Density is represented as g/ml or g/cm3, or any conversion there of. Now that you have both the table of masses and table of volumes filled out, calculate the density of the objects measured. Record your results in the table of densities.

Table of Densities

Object	Pebble	Wooden dowel	Wooden block	Glass ball	Copper ball
Density in (g/cm³)
Volume in (g/ml)

Follow-up questions

How did the densities compare to each other, and were there any that surprised you?
What units would you use to describe the density of lead?
If you have chunk of gold and you want to know how pure it is how would you go about doing that?

Temperature

In the metric system we use degrees Celsius (ºC) most often, but in some cases we Kelvin (K) to measure temperature. There are some instances in science where degrees Fahrenheit (ºF) are used instead of ºC. Fundamentally temperature is a measure of the kinetic energy of molecules or how much the molecules are moving at the atomic level. The higher the temperature the more the molecules are moving, and is what gives us the primary states. Solids have molecules that barely move, liquids molecules move freely, gasses molecules move freely and to a much greater degree than liquids.

The degrees Celsius scale were modeled after the changes of state of matter of water. Freezing/melting point of water is at 0ºC, and the boiling/condensing point of water is at 100ºC. This compares to 32 ºF and 212 ºF in the degrees Fahrenheit scale. We can switch between the two scales by using the following formulas:

ºC = (ºF -32)/1.8 and back using ºF = (1.8ºC) + 32

The primary difference between Celsius and Fahrenheit is how fine of a scale they are. In ºC between the temperature of freezing to boiling is just 100º while between the same points in ºF there are 180º. This makes Fahrenheit a finer scale to use when measuring temperature, similar to how mm are a finer scale than m.

Experimental procedure

Using a thermometer find the temperatures of several items around the room in ºC, and make sure to allow time for the thermometer to register the temperature.

Room temperature = ºC. Surface of your skin = ºC

Cold tap water = ºC. Hot tap water = ºC and ice water = ºC

Follow-up questions

When would you expect using ºF would be better suited for scientific measurements?
Did you notice the comparison between normal room temp and body temp in both ºC and ºF, what are the approximate equivalent temperatures for each?

Licensing and Attributions

This lab titled “How we measure in Science” is shared under CC BY-SA 4.0 License and was authored by Tyler Wilson (Oxnard College).

Search

Text Color

Text Size

Margin Size

Font Type