## Key Concepts

- Recalling what are whole numbers and decimals
- Use models and strategies to multiply
- Multiply the decimals by the power of 10
- Patterns in multiplying decimals by power 10
- Estimate the products of a decimal and a whole number

## Introduction

### Use models and strategies to multiply decimals:

**Whole Number Multiplication:**

By using multiplication, we can find the product of two whole numbers.

E.g.

**Rounding the decimals:**

To round the decimals, we have to follow certain **rules** and we have to know the **place values **of decimal number.

E.g.

### Multiply Decimals by Power of 10

Multiplying a decimal by 10 moves the decimal point one place to the right. For each zero in the power of 10, move the decimal point one place to the right.

Exponent: Exponents are often known as powers or indices. It is the quantity that represents the power to which the number is raised.

E.g. (Here is 100. So decimal point moved two times to the right and 2 is the exponent).

Try this:

- 0.084 x 10
^{2}

- 1.652 x 10
^{3}

### Patterns in Multiplying Decimals by Power of 10

Two patterns can be discussed here to know more about the multiplication of decimals by power 10.

- By using Place value chart – Pattern appears when its multiplied.

- Another pattern appears by holding the numbers.

{Here, the digit in one’s place is moved to the left when it is multiplied by the power of 10}.

### Estimate Products of Decimals and Whole Numbers

To estimate the product of decimals and whole numbers, we are using two types of methods.

**Rounding Numbers/overestimate**: First round off the multiplier and the multiplicand to the nearest tens, hundreds, or thousands and then multiply the rounded numbers and When the estimate is higher than the actual value, it’s called an overestimate.

**Example:**

**Compatible numbers**/**Underestimate**: The numbers that are easy to add, subtract, multiply, or divide mentally come under this. Compatible numbers are close in value to the actual numbers that make estimating the answer and computing problems easier, and when the estimate is lower than the actual value, it’s called an underestimate.

**Example:**

**Example: **

- Estimate the product of 5.57 and 6 by using two methods.

**Try this:**

- Estimate the product of 0.77 and 16 by using two methods.

- Estimate the product of 46.3 and 6 by rounding method.

- Estimate the product of 84.5 and 8 by compatible method.

**Let’s Check Your Understanding:**

- Write the example for rounding the number of two-digit number.

- What did you observe about the decimal number when you are multiplying the power of 10?

- What is meant by power?

- What do you understand by the definition of estimation?

### What we have learnt

- Use patterns and mental math to understand the simple multiplication of decimals with power 10.
- Observe the decimal point position while using types of pattern for multiplication.
- When doing the estimation at rounding the number and compatibility, cross check with the actual value.

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