## Key Concepts

- Rounding and estimation for products

**Prior Knowledge:**

Look at the picture and answer the following questions:

Mark wants to buy a T-shirt.

He knows that his chest size is 37 cm.

Can you help him in choosing the correct size of T-shirt?

**Answer:**

The T-shirt’s size is 40.

**Estimation**

Find the number that is close to the right answer.

- We do not try to get the exact answers.
- What we want is something that is close to the right answer.

Estimation will save your money. Always do a quick estimation of how much you should pay:

Estimation will save your time.

**Example: **

Alisha and Mike collected marbles.

Alisha has collected 335, and Mike has collected 442 marbles.

Choose an estimate to find the number of marbles they collected together.

**Solution:**

The estimate is obtained by rounding off the digits to their nearest tens.

To get an estimate of the sum, round off all the numbers to the same place value and add them.

Number of marbles collected by Alisha = 335 rounded off to 340

Number of marbles collected by Mike = 442 rounded off to 440

Total number of marbles = 340 + 440 = 780

The estimated answer is 780

**3.2 Estimate products**

**The rules for rounding:**

**Rule1: If the number you are rounding is followed by 2, 3, 4, 5, or 6, round the number up**

**Example:** 38 rounded to the nearest ten is 40.

**Rule 2: If the number you are rounding is followed by 3, 4, 5, 6, or 7, round the number down.**

**Example:** 33 rounded to the nearest ten is 30.

### Let us understand the meaning of estimation of products

You can estimate a product by first rounding the factors to the nearest ten, hundred, or thousand, then find a product that gives the exact answer.

Let us recite a poem on rounding.

**3.2.1 Rounding and estimation for products**

**Rounding to 10: **

Rules for rounding off to the nearest 10:

Rule1: While rounding off to the nearest ten, if the digit in the units place is between 0 and 4, which is less than 5, then the unit digit is replaced by 0.

Rule2: If the digit in the units place is 5 to 9, i.e., > or 5 but < 10, then the units place is replaced by ‘0’, and the tens place increased by 1.

**Example1: 64 rounds to nearest 10.**

**Example1: From the below figure, ….**

**Rounding to 10 for product: **

**Example1: **Estimate the products of 3 and 56.

3 ⟶ 3

56 ⟶ 60. 56 rounded up to 60

Calculate mentally 3 × 60 = 180

The estimated product is 180

**Examples of rounding to 100:**

Let us observe the following examples on rounding to the nearest 100.

**Rounding to 100 for product:**

**Example1: **Estimate the product of 7 × 161

**Step1:** 161 rounds off to 200

**Step2:** The estimated product = 7 x 200 =1400.

**Example2:** Estimate the products of 4 and 267 by rounding to the nearest hundred.

267 is close to the 300,

267 ⟶ 300

4 × 300 = 1200

The estimated product is 1200.

**Example3:** Each question on a game show is worth 4 points. There are 602 questions in each episode of the show. Find the total points per episode. What is a good estimate?

Multiply:

4× 602 =?

Round the second factor to the nearest hundred.

4 x 602=?

4 x 600= 3,600

3,600 points is the good estimate.

#### Rules for rounding off to the nearest 1000:

Rule I: While rounding off to the nearest thousand, if the digit in the hundreds place is between 0 and 4, which is less than 5, and the hundreds place is replaced by ‘0’.

Rule II: If the digit in the hundreds place is equal to or greater than 5 and the hundreds place is replaced by ‘0’, and the thousands place is increased by 1.

**Rounding to 1000 for product:**

**Example1: **Estimate the products of 3 and 6654 by rounding to the nearest thousand.

**Solution:**

6654 is close to the 7000

6654⟶7000

3× 7000 = 21,000

The estimated product is 21,000

**Example1: Round 5,479 to nearest 1000.**

Solution:

We choose the two multiples of 1000 just greater than and just less than **5,479** on the number line.

We observe that **5,479** is closer to **5,000**.

So, it is rounded down to **5,000**.

**Example2: Round off 2,804 to the nearest 1000.**

Solution:

We choose the two multiples of 1000 just greater than and just less than** 2,804** on the number line.

We observe that **2,804** is closer to **3,000**.

So, it is rounded down to **3,000**.

## Exercise

- Estimate the product of 99 × 7
- Estimate to find the product of 398 × 6
- What is the best estimate for Klein to determine the difference of $19,320 and $9,876?
- Round to the nearest hundredths place: 9,765.248
- Estimate the product, round the first factor to the greatest place value and then multiply the following 65 × 4 =?
- The International Space Station takes 644 minutes to orbit Earth 7 times. About how long does each orbit take?
- What is the place value of 5 in 234,567?
- Use rounding or compatible numbers to estimate the product.

3544 × 5 - Round to the nearest thousand place: 6,56,999.
- Write the place value of each number: 23, 45, 654

### Concept Map:

### What we have learned:

- Understanding the estimation
- Cost of estimation
- Rules for rounding
- Rounding to the nearest 10, 100, 1000