**Nikhilam Sutra for Multiplying by Base:**

 Certainly! Let's delve into the Nikhilam Sutra for multiplying by the base. This technique is particularly useful when you're multiplying a number by a base like 10, 100, 1000, and so on.

1. Choose the base you want to multiply by (e.g., 10, 100, 1000, etc.).

2. Subtract the original number from the chosen base.

3. Multiply the result by the number you want to multiply by the base.

4. Add the original number to the product obtained in step 3.

**Example:**

Let's multiply 356 by 100 (base of 100) using the Nikhilam Sutra:

```

  Base: 100

  Number: 356

  Difference from Base: 100 - 356 = -256

  -256 (Difference) × 100 (Number to multiply by the base) = -25600

  -25600 + 356 (Original number) = -25244

  Multiplying 356 by 100 = -25244

```

In this example, we multiplied 356 by the base 100 using the Nikhilam Sutra. This technique helps simplify the multiplication process by focusing on the difference from the base and the multiplication of that difference by the chosen number.

Of course! Let's explore more examples of multiplying by a base using the Nikhilam Sutra.

**Example 1: Multiplying by 1000 (Base of 1000)**

Let's multiply 427 by 1000 using the Nikhilam Sutra:

```

  Base: 1000

  Number: 427

  Difference from Base: 1000 - 427 = 573

  573 (Difference) × 427 (Number to multiply by the base) = 244371

  244371 + 427 (Original number) = 244798

  Multiplying 427 by 1000 = 244798

```

**Example 2: Multiplying by 10 (Base of 10)**

Let's multiply 96 by 10 using the Nikhilam Sutra:

```

  Base: 10

  Number: 96

  Difference from Base: 10 - 96 = -86

  -86 (Difference) × 96 (Number to multiply by the base) = -8256

  -8256 + 96 (Original number) = -8160

  Multiplying 96 by 10 = -8160

```

**Example 3: Multiplying by 100000 (Base of 100000)**

Let's multiply 812 by 100000 using the Nikhilam Sutra:

```

  Base: 100000

  Number: 812

  Difference from Base: 100000 - 812 = 99188

  99188 (Difference) × 812 (Number to multiply by the base) = 80478656

  80478656 + 812 (Original number) = 80479468

  Multiplying 812 by 100000 = 80479468

```

The Nikhilam Sutra for multiplying by a base simplifies the multiplication process by considering the difference from the base and the multiplication of that difference by the original number. This technique is especially useful for quickly multiplying by powers of 10 and simplifying large calculations.