Math Antics - Measuring Distance

Summary

In this Math Antics video, Rob teaches viewers how to use units of measurement in real-life scenarios, focusing on centimeters and inches. He explains the use of rulers, the importance of accuracy, and how to read measurements down to millimeters and fractions of an inch. The video also touches on the metric system's simplicity compared to the traditional American system, which uses fractions based on powers of two. Rob concludes by introducing low-tech devices like tape measures and measuring wheels for longer distances, encouraging viewers to practice measuring to improve their math skills.

Takeaways

• 📏 Measuring distances is a fundamental skill taught in both science and math classes, using units like centimeters and inches.
• 📏 A ruler is a flat tool with standardized markings for measuring lengths, often in both metric (cm) and imperial (inches) units.
• 📏 For accuracy, rulers are divided into smaller units like millimeters (1/10 of a centimeter) and fractions of an inch.
• 📏 To measure an object, align the zero mark of the ruler with one end of the object and read the other end's position on the scale.
• 📏 When an object's end doesn't align with a full mark, use the subdivisions to estimate the length more precisely.
• 📏 Advanced measuring tools like calipers and micrometers can provide measurements with higher accuracy, down to nanometers.
• 📏 The metric system divides units into tenths, making it easier to use with the decimal system, whereas the imperial system uses more complex fractions.
• 📏 Inches can be subdivided in two ways: by ten (like the metric system) or by two (traditional American system), each with its advantages and challenges.
• 📏 Memorizing common fraction-to-decimal conversions can help when working with traditional fractions of an inch.
• 📏 Low-tech devices like tape measures and measuring wheels are useful for measuring longer distances, with the latter tallying the distance as it's rolled.
• 📏 High-tech methods and devices, including smartphones, can also measure distances, offering convenience and additional tracking capabilities.

Q & A

What is the primary focus of the video?

The primary focus of the video is to teach how to use common units for measuring distances in real-life situations, emphasizing the use of rulers and the importance of accuracy in measurement.

Why might one use their finger to measure an object like a pencil?

Using one's finger to measure an object is a rudimentary method that relies on the approximate width of a pinky finger as a unit of measurement. It's mentioned for its simplicity but also to highlight the need for more accurate tools like rulers.

What is a ruler and how does it help in measuring distances?

A ruler is a flat piece of material marked with standard units of distance. It helps in measuring distances by aligning one end of the object with the zero mark and reading the position of the other end on the scale.

How can one get a more accurate measurement of an object using a ruler?

To get a more accurate measurement, one can use the subdivisions of the main units on the ruler, such as millimeters for centimeters or fractions of an inch for inches, to estimate the measurement between the main marks.

What is the significance of the ruler's subdivision marks, and how are they used?

The ruler's subdivision marks, which represent smaller units like millimeters, allow for more precise measurements. They are used by aligning the object's end with these marks to estimate lengths that fall between the main scale marks.

Why is accuracy important in measurement?

Accuracy is important because it refers to how close a measured value is to the true value. In practical applications, being accurate ensures that measurements are as close as possible to the actual dimensions of an object.

What are some limitations of using a standard ruler for measurements?

A standard ruler has limitations in terms of the smallest unit it can measure, usually millimeters for centimeters or fractions of an inch. It cannot provide measurements with higher precision without using additional tools or estimation techniques.

How do you measure an object's length in inches using a ruler?

To measure an object's length in inches, align one end of the object with the zero inch mark on the ruler, and observe where the other end lies on the inches scale. Subdivisions of inches can be used for more accuracy.

What are the two common ways of subdividing inches on a ruler, and how do they differ?

The two common ways of subdividing inches are by dividing by 10, which results in tenths, hundredths, etc., and by dividing by 2, which results in halves, quarters, eighths, and so on. The first method is similar to the metric system and is easier to convert to decimals, while the second is more traditional and can be more challenging to work with in decimal form.

What are some low-tech devices used for measuring longer distances?

Low-tech devices for measuring longer distances include tape measures, which are flexible rulers on a spool, and measuring wheels, which tally the distance as they are rolled along a surface.

What is the humorous advice given at the end of the video regarding practicing math?

The humorous advice given at the end of the video is to 'brush up' on fractions to be successful at measurement, which is a play on words since the video also discussed measuring a toothbrush.

Outlines

00:00

📏 Introduction to Measurement Units and Accuracy

Rob from Math Antics introduces the concept of measuring distances using units like centimeters and inches. He explains how to use a ruler to measure the length of a pencil in centimeters, highlighting the importance of accuracy. The ruler is described as a flat material with markings for standard units of distance. The video demonstrates how to align the ruler with the object and read the measurement. It also addresses the issue of measuring objects that don't align perfectly with the ruler's marks, introducing the concept of millimeters for more precise measurements. The limitations of measurement accuracy based on the device used are discussed, and the idea that exact measurements are impossible is introduced.

05:00

📏 Advanced Measurement Techniques and Fractions

The script continues with a discussion on how to achieve greater accuracy in measurements, particularly when dealing with objects that don't align with whole numbers on a ruler. It explains the use of millimeters and the concept of estimation to get closer to the true value. The video then transitions to measuring in inches, comparing the metric system's simplicity with the traditional American system's use of fractions. It outlines two common ways of subdividing inches: one based on dividing by 10 (similar to the metric system) and the other based on dividing by 2, which is more complex. The script humorously attributes the complexity of the American system to historical monarchies and suggests that viewers may need to 'brush up' on their fractions to be proficient in measurements.

10:03

🛠️ Low-Tech Devices for Measuring Longer Distances

In the final paragraph, Rob introduces low-tech devices for measuring longer distances, such as tape measures and measuring wheels. Tape measures are described as flexible rulers that can be wound up for convenience and used to measure longer objects like wood for carpentry. Measuring wheels are explained as devices that roll along a surface, tallying the distance traveled in feet or meters, which is useful for measuring large outdoor distances. The video concludes with a reminder of the importance of practice in mastering math and measurement skills, and encourages viewers to practice measuring various objects.

Keywords

💡Measurement

Measurement is the process of determining the size, amount, or degree of something. In the video, measurement is central to understanding how to use units of distance to quantify the length of objects such as a pencil or a toothbrush. The script explains how to use rulers to measure in centimeters and inches, highlighting the importance of measurement in both science and math.

💡Centimeter

A centimeter is a unit of length in the metric system, equal to one hundredth of a meter. The video uses the centimeter as an example of how to measure the length of a pencil, showing that it is roughly the width of a pinky finger and aligning the zero mark of a ruler with one end of the pencil to read the length in centimeters.

💡Ruler

A ruler is a flat, straight-edged instrument used for measuring lengths. In the context of the video, a ruler is a tool marked with standard units of distance, such as centimeters and inches. The script describes how to use a ruler to measure the length of an object by aligning the zero mark with one end of the object and reading the measurement at the other end.

💡Millimeter

A millimeter is a unit of length in the metric system, equal to one thousandth of a meter or one-tenth of a centimeter. The video explains that rulers often divide the space between centimeter marks into 10 equal parts representing millimeters, allowing for more precise measurements. For instance, the sharpened pencil's length is given as 17.3 cm, indicating 17 centimeters and 3 millimeters.

💡Accuracy

Accuracy in measurement refers to how close a measured value is to the true value. The video emphasizes the importance of accuracy by showing how to estimate measurements beyond the smallest marked unit on a ruler, such as estimating the pencil's length to be closer to 17.31 cm rather than exactly 17.3 cm.

💡Inch

An inch is a unit of length in the imperial and US customary systems, equal to 2.54 centimeters. The video discusses measuring in inches as an alternative to the metric system, using a toothbrush as an example and showing how to read measurements between the inch marks on a ruler.

💡Fraction

A fraction represents a part of a whole, expressed as one quantity divided by another. In the video, fractions are used to express measurements that do not align exactly with whole units, such as 7 and two-eighths of an inch. The script explains how fractions are necessary for increased accuracy in measurement, especially when dealing with traditional units like inches.

💡Calipers

Calipers are precision measuring instruments used for measuring the distance between two opposite sides of an object. The video mentions calipers as an example of a device that can provide more accurate measurements than a standard ruler, capable of measuring to a tenth or even a hundredth of a millimeter.

💡Tape Measure

A tape measure is a flexible ruler, often made of fabric or metal, that can be extended and retracted for measuring longer distances. The video describes tape measures as a convenient tool for carpenters and others who need to measure longer objects, as they can be wound up compactly for storage.

💡Measuring Wheel

A measuring wheel, also known as a wheel measure or distance wheel, is a device used to measure longer distances by rolling it along the ground. The video briefly introduces measuring wheels as a tool for measuring distances longer than what can be conveniently managed with a tape measure, with a counter that tallies the distance rolled.

Highlights

Introduction to using units of measurement in real-life scenarios.

Explanation of how to measure an object's length using a ruler.

Demonstration of measuring a pencil's length in centimeters.

Discussion on the importance of accuracy in measurements.

Introduction to millimeters as a subdivision of centimeters for increased accuracy.

Practical example of measuring a sharpened pencil to a more precise length.

Estimation techniques for measurements beyond the ruler's smallest unit.

Mention of advanced measurement tools like calipers and micrometers.

Philosophy of measurement and the inherent limits of accuracy.

Transition to measuring in inches using the non-metric side of a ruler.

Tutorial on measuring a toothbrush's length in inches.

Explanation of how inches are subdivided into fractions for greater precision.

Comparison between the metric system's simplicity and the complexity of traditional American units.

Introduction to the metric-like subdivision of inches by tenths.

Discussion on the traditional subdivision of inches by powers of two.

Practical example of measuring a toothbrush using a ruler with sixteenth-inch markings.

Introduction to low-tech devices for measuring longer distances like tape measures and measuring wheels.

Encouragement to practice measuring to improve math skills.

Transcripts

Hi I’m Rob, welcome to Math Antics!

In a previous video, we learned about the most common units for measuring distances.

In this video we’re gonna talk about how you actually use some of those units

when making a measurement in real life.

Making measurements is something you’d typically learn how to do in science class,

but since measurement uses math to get the job done,

it’s often taught in math class too. So here we go…

Suppose we’re given an object, like this pencil,

and we’re asked to measure its length in centimeters.

To do that, we’d need some method or device that will tell us

how many centimeters long the pencil is.

Remembering that a centimeter is roughly the width of a pinky finger,

I could just use my finger as that device and

see how many finger-widths it takes to get from one end of the pencil to the other,

but something a little more accurate would be nice.

And that’s where a ruler comes in handy!

I, the great King Rob, ruler of all the land,

declare that the span of my royal hand shall henceforth be the measure

of all things in my kingdom great or small.

Uhhh… not that kind of a ruler.

In math and science, a ruler is a flat piece of material

that has markings on it that correspond to standard units of distance.

For example, this ruler has a series of markings that correspond to

inches on one side and centimeters on the other.

That’s cool, we’ll just ignore the inches side and use the centimeter side for this measurement.

We start by moving the ruler so that the zero centimeter mark

is aligned as closely as we can with one end of our pencil.

Then, we’ll see where the other end of the pencil lies on the scale of centimeters.

Looking at the numbers, you can see that the other end lines up nicely with the 19 cm mark.

So this pencil is 19 cm long.

But what if the pencil gets sharpened and then used

and sharpened and used again so that it gets shorter?

Now if we re-measure it with our ruler, you’ll see that we have a small problem.

The tip of the pencil doesn’t line up with any of the centimeter marks anymore.

It lies somewhere between the 17 and 18 cm marks.

We could just say that it’s between 17 and 18 cm long,

but it would be nice if we could be a little more accurate than that.

Being more accurate means making a measurement that is closer to the true value.

Fortunately, most rulers divide the space between each centimeter mark

into 10 equal parts that represent millimeters which are exactly one-tenth of a centimeter.

Because the millimeter marks are so much smaller, they don’t have numbers on them,

but if you look closely, you’ll be able to count that there are 9 smaller lines

that divide the centimeter into 10 equal parts.

The middle of these 9 lines is usually a little longer than the rest

so that it’s easier to tell where the halfway point is.

Using these subdivision marks,

we can get a more accurate measurement of the length of our sharpened pencil.

Do you see how the pencil’s tip almost lines up with the third subdivision line

that comes right after the 17 cm mark?

That means that the length of the pencil is 17 cm plus 3 mm or 17.3 cm.

Well, that’s a pretty close measurement.

But remember the tip of the pencil didn’t line up exactly with the third subdivision line.

It went just a little bit past it.

Our ruler doesn’t have markings smaller than a millimeter,

so it will be hard for us to make a measurement more accurate than that, but we could make an estimate.

For example, it looks like the pencil tip goes past the 3 mm mark by a very small amount,

maybe just a tenth of a millimeter,

so we could estimate that its length is closer to 17.31 cm.

If you really did need a more accurate measurement,

you’d need to use a better measurement device that could provide that level of accuracy.

For example, calipers and micrometers are devices that can measure distances

as accurate as a tenth or even a hundredth of a millimeter.

And certain measurement techniques using lasers can achieve even higher accuracies

down to extremely small units like nanometers.

Those more advanced types of measurements are beyond the scope of this video,

but hopefully they’ll help you realize something fundamental about the nature of measurement.

You can’t measure the EXACT value of something.

There’s always a limit to the accuracy you can achieve based on your measurement device.

Accuracy is basically how close a measured value is to the true true value.

And in measurement the idea is to get as close as possible,

or at least as close as you need for your purposes.

Luckily, I didn’t really need to know the length of this pencil down to the nearest tenth of a millimeter.

In fact, I didn’t really need to know it’s length at all since I’m just gonna write with it.

Okay, now that you understand what accuracy is,

and we’ve made a measurement that was accurate to the nearest centimeter

as well as one that was accurate to the nearest millimeter,

lets try making a measurement with the non-metric side of our ruler, which measures inches.

Suppose we want to know the length of this toothbrush in inches.

To measure that, we first line up one end of the toothbrush

with the start of the inches scale on the ruler which represents zero inches.

Then we see where the other end of the toothbrush lies on that scale.

Notice it’s somewhere between 7 and 8 inches.

Can we get a more accurate measurement than that?

Yep! Fortunately, as was the case with centimeters on the other side of the ruler,

inches are usually subdivided into fractions of an inch also.

On this particular ruler, each inch is subdivide into 8 equal parts.

That means our toothbrush is not quite as long as 7 and three-eighths of an inch

but it’s a little longer that 7 and two-eighths of an inch,

which would be equivalent to 7 and one-quarter inches.

Whoa, whoa, whoa… what are you talking about with all these fractions?

I thought this video was about measurement, not fractions!

Well yes, but when things don’t line up exactly with a particular unit,

to get more accuracy you need to use fractions of that unit.

The metric system makes that look easy, because things are always divided by 10,

so the fractions match up really nicely with our base-10 decimal system.

But English or American units have traditionally been divided up differently,

so the fractions you use for them are a little bit trickier.

So, you’re saying this is all America’s fault.

Well, America didn’t invent the system.

It’s just a traditional system of units that goes way back in history to the days of monarchies,

so I guess it’s probably some kings fault.

[Gasp] How dare you!!

Anyway, it’s true that the traditional way of subdividing inches

is kinda messy when compared to the metric system,

so it will help if we take a closer look.

Basically, there’s two ways that inches are commonly subdivided;

one is based on dividing by 10

and the other is based on dividing by 2.

We’ll start with the system that’s based on dividing by 10

because that sounds a lot like the metric system, doesn’t it?

It turns out that an inch can be divided up in a metic-like way,

even though an inch is not a metric unit.

Here’s how that works…

You start with an inch and then divide it into 10 equal parts.

Each mark represents a tenth of an inch,

so you could express the fractional parts easily with decimal digits,

just like you do with the metric system.

For example, if a measurement came out to be one and two-tenths inches,

you’d just say it’s 1.2 inches.

Or if a measurement came out to be five and eight-tenths inches,

you’d just say it’s 5.8 inches.

And when you need more accuracy, you can keep sub-dividing by 10

so that you’d get hundredths of an inch,

thousandths of an inch,

ten-thousandths of an inch and so on.

This way of dividing up inches is commonly used in American engineering

since it has many of the benefits of the metric system, even though it’s based on inches.

The other way of dividing up inches, which is still commonly used in American construction,

is to divide them up by two.

Here’s how that system works…

You start with an inch and then divide it into two equal parts.

That means you can now measure to an accuracy of half an inch.

Then you divide those half-inches by two

so you can measure to an accuracy of a quarter of an inch.

Then you divide those quarter-inches by two

so you can measure to an accuracy of an eighth of an inch.

And you keep going like that.

Dividing by two again lets you measure to an accuracy of a sixteenth of an inch.

And dividing by two again lets you measure to an accuracy of a thirty-second of an inch, and so on…

The bases of these fractional parts of an inch are all different,

but they are all powers of 2.

It’s actually a really logical system if you think about it,

but it has the disadvantage that it’s harder to convert to decimal values when you need them.

It’s also harder to add and subtract measurements if the fractions don’t have the same base.

When things are divided by 10, it’s easy because we use decimal number places

that are specifically designed for counting fractions like tenths, hundredths and thousandths.

But we don’t have number places for halves, quarters and eights.

Instead, it’s very common for people who use a lot of these traditional fractions of an inch

to just memorize some of the most common equivalent decimal values

and use a calculator to convert the rest.

For example, they might memorize things like:

1/2 = 0.5,

1/4 = 0.25,

and 1/8 = 0.125

Now that you know the two main ways of dividing up inches,

let’s go back to our toothbrush example.

If we use a ruler that has division of a sixteenth of an inch,

you can see that it’s length is about 7 and five-sixteenths of an inch.

That should be plenty accurate for brushing my teeth!

So now you know the basics of how you use a ruler to make measurements,

but you may need to “brush up” on your fractions to be successful at it.

See what I did there?

Last of all, I want to briefly introduce you to some low-tech devices

that are commonly used to measure longer distances.

For example, a tape measure is sort of a long flexible ruler

that can be wound up on a spool to make it more compact.

It’s a really handy device and carpenters use them all the time.

When you unwind it, you can measure much longer distances in the same way you would with a ruler.

And it’s a lot more convenient than carrying around a 10 meter stick!

There’s another cool device, often called a “measuring wheel”,

that can be used to measure even longer distances by rolling a wheel along the ground (or any surface).

It has a counter on it that tallies up each foot or meter that you roll it past

so you can measure the total distance traveled.

Of course, there are lots of high tech methods for measuring distances nowadays too,

and your phone can probably keep track of how many miles you’ve traveled in a day,

and where you went…

and who you talked to…

and what you might like and might want to buy…

...and...and who you have a crush on and…

Alright, that’s the basics of measuring distance.

Remember, the way to get good at math is to actually practice it,

so get on out there and start measurin’ stuff!

As always, thanks for watching Math Antics, and I'll see ya next time!

You heard the man. Practice!

Learn more at www.mathantics.com