Estimation & Approximation: Solving Rounding To Significant Figure Word Problems

Introduction

Welcome to another Math blog post on the topic of Estimation & Approximation!

In a previous blog post, we discussed how to solve word problems about the largest and smallest possible values of a rounded number. Click on this link to check it out if you haven’t!

In this blog post, we will discuss how to tackle similar word problems involving rounding to significant figures.

Let’s Take A Look At This Estimation & Approximation Question

Thought Process

The question wants you to find the largest and smallest possible number of people at the stadium.

It is given that there are 48 000 people in the stadium. But is that the exact number? No.

The question tells us that this number was rounded to 2 significant figures.

Some students would get stuck at this point and tell me, “Teacher, I really don’t know what to do. If you said round it off to the nearest thousands, I’d know what to do. But 2 significant figures, I am not sure!”

Are you also confused about what 2 significant figures mean?

Don’t worry because I will teach you the secret to unlocking such questions.

First, write down 48 000.

Remember that we are rounding off to 2 significant figures.

The first digit in the number is 4, and this is our first significant figure!

What is the second digit? It is 8! Therefore, this is our second significant figure.

After identifying the second significant figure, we can proceed to determine its place value.

What is the place value of the digit 8? It is thousands!

🚀 Tip For Rounding To Significant Figure Word Problems 🚀

The key to unlocking this question is finding the 2nd significant figure is in the thousands place before we can even do anything.

The next step is to draw a number line and write 48 000 in the middle.

To get the number on the right, add 1 000 to 48 000.

To get the number on the left, subtract 1000 from 48 000.

Now, let us find the numbers in the middle.

What is the number in the middle of 47 000 and 48 000? It’s 47 500! That is our first middle number.

Next, what is the middle of 48 000 and 49 000? It’s 48 500. We can now add it as our second middle number.

Now that we have all these information in our number line, we can start solving the question.

In the previous blog post, we mentioned that the number that you see on the left side of your rounded value will always be the smallest possible number.

Let us check. Is 47 500 really the smallest possible number?

🔎 Remember This When Rounding A Number To 2 Significant Figures 🔎

Look at the 3rd significant figure. When the number is 5 and up, you will round up. When it is 4 and below, you will round down.

In order to round it off to 2 significant figures, we have to look at the 3rd significant figure, which is 5. This means 7 will be rounded up to 8. Therefore, we will get 48 000, which is what we are looking for!

The next question we have to ask is, can the number get any smaller?

Let’s try going one digit smaller and check 47 499.

When we round it off to 2 significant figures, we will get 47 000, which is not what we are looking for.

Therefore, we can confirm that the smallest possible value is 47 500.

Let us proceed to finding the largest possible number. Is it the number on the left of 48 000, which is 48 500? Let’s check!

To round off 48 500 to 2 significant figures, we have to look at the 3rd significant figure, which is 5. It will cause 8 to round up, so we will end up with 49 000.

Is this what we are looking for? No, right? Remember that we are looking for 48 000.

Definitely, 48 500 is not the largest possible value.

Should we go bigger or smaller?

Let’s try going one number bigger — 48 501.

Will this give us 48 000 when rounded off to 2 significant figures?

The 3rd significant figure is 5, which causes 8 to round up. We will get 49 000, which is not what we want.

Now that we know that we cannot go bigger, let’s try going one number smaller, which is 48 499.

Let’s check!

The 3rd significant figure is 4, which will cause the 2nd significant figure to round down, giving us 48 000.

This is exactly what we are looking for.

Therefore, the largest possible value is 48 499.

Suggested Answer

The smallest possible value is 47 500, while the largest possible value is 48 499.

Conclusion

I hope that you’ve learned how to find the smallest and largest possible value of a number rounded to a given significant figure better and faster!

Remember that the first thing you have to do is to identify the place value of the number in the given significant figure — in our example, the 2nd significant figure in 48 000 is 8, which is in the thousands place.

Once you know this information, you can proceed to draw a number line and add the two numbers on the left and two numbers on the right.

From there, you can check for the smallest and largest possible values!

Stay tuned for more Secondary 1 Math blog posts!