Introduction

How do you approach Math questions asking you to find the smallest and largest possible value of a rounded number?

I noticed that most of my students would guess the answers. Is this how you would solve Estimation & Approximation problems too?

In this blog post, I will share a more efficient way you can use to tackle Estimation & Approximation questions so you wouldn’t have to guess the answer!

Let’s Find The Keywords In This Question

First, let us look for the keywords in the question.

Read the first sentence: The population of Tiong Bahru in 2019 was 13 000, correct to the nearest thousand.

The keyword here is the population in Tiong Bahru in 2019 — 13 000, correct to the nearest thousand.

Now, read the second sentence: What was the largest and smallest possible value of the population of Tiong Bahru at the given time?

What does the question want us to find?

It is asking for the largest and smallest possible value of the population of Tiong Bahru.

There are different ways for you to solve this question. Most students would try to solve this by guessing the largest and smallest possible values.

However, I will teach you an efficient way of tackling this question!

Rounding Word Problem Using A Number Line

Start by drawing a number line.

Because the population is rounded off to 13 000, we will write it in the middle of our number line.

The given information in the question tells us that 13 000 has been rounded off to the nearest thousand so we will add 1 000 to get the figure on the right.

13 000 + 1 000 = 14 000

Next, we will subtract 1 000 from 13 000 to get the figure on the left.

13 000 – 1 000 = 12 000

Now that we have the numbers at the both ends of our line, I want you to find the middle number between 12 000 and 13 000.

It is 12 500!

Do the same thing for 13 000 and 14 000.

It is 13 500!

Write them down in our number line.

Now that we have these numbers, we can start finding the smallest possible value.

Finding The Smallest Possible Value

12,500 is smaller than 13 500 so the smallest possible value is likely to be 12 500.

Is 12 500 the smallest possible value such that when 12 500 is rounded off to the nearest thousand, it should give me 13 000? Let’s check!

🔎 Remember This When Rounding A Number Off To The Nearest Thousand 🔎

Look at the digit in the hundreds place. When the number is 5 and up, you will round up. When it is 4 and below, you will round down.

Let’s look at 12 500.

Because the number in the hundreds place is 5, it will cause the digit in the thousands place to round up. So, we will get 13 000.

But is this the smallest value? Let’s try going one number smaller — 12,499.

What is 12 499 when rounded off to the nearest thousand?

Again, look at the digit in the hundreds place. It is 4, so we need to round down, giving us 12 000, which is not what we are looking for.

Therefore, we have confirmed that the smallest possible value is 12 500.

↔️ Tip To Find The Smallest Possible Value Using A Number Line ↔️

Whenever you draw a number line, the first number that you will see in the left side of your rounded off value will always be the smallest value.Answer For Part (A)

Finding The Largest Possible Value

If the smallest possible value is the number on the left of 13 000, is the highest possible value the number on the right, which is 13 500?

Let us check by rounding off 13 500 to the nearest thousand.

The number in the hundreds place is 5, which means we should round up. Therefore, we will get 14 000.

Remember that the value should be 13 000 when rounded off to the nearest thousand, so this is wrong!

Should we then go bigger or smaller than 13 500? Do we check 13 501 or 13 499?

Recall that when we rounded 13 500 off, it already gave us 14 000. When we take 13 501, we will get the same thing.

This means that you cannot use more than 13 500, so let us go smaller and take a look at 13 499.

Let us round off 13 499 to the nearest thousand.

The number in the hundreds place is a 4, so we are going to round down. We will get 13 000, which is what we are looking for.

Therefore, the largest possible value is 13 499.

Conclusion

After reading this blog post, I hope that you have learned that instead of guessing the value of a rounded number, you can draw a number line to find the smallest and largest possible values of a rounded number.

↔️ Tip When Using A Number Line For Rounding Word Problems ↔️

Look at the number on the left side of the number line to check for the smallest possible value and the right side of the number line for the largest possible value.

Keep a lookout for more Estimation & Approximation blog posts!

If you like our methodology, we've some ongoing weekly Math classes: