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Chapter 0: Problem 39

Multiply or divide as indicated. \(123.26 \times 10\)

Short Answer

Expert verified
1232.6

Step by step solution

01

- Understand the Operation

In this problem, the operation required is multiplication. We need to multiply the number 123.26 by 10.
02

- Recall the Rule for Multiplying by 10

When a number is multiplied by 10, the decimal point moves one place to the right. For example, multiplying 3.5 by 10 gives 35.
03

- Move the Decimal Point

Move the decimal point in 123.26 one place to the right. This turns 123.26 into 1232.6.
04

- Write the Final Answer

After moving the decimal point, the final result of multiplying 123.26 by 10 is 1232.6.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

decimal point movement
When multiplying a number by 10, the decimal point shifts one spot to the right. This rule is consistent and helps make multiplication easier. Moving the decimal point adjusts the place value of each digit, effectively making the number ten times larger. For instance, if you start with 3.5 and multiply by 10, the result is 35. This happens because the decimal moved from between the 3 and the 5 to the right of the 5, changing the number from 3.5 to 35.
In our exercise, we see this with 123.26. By shifting the decimal point one place to the right, it becomes 1232.6. This rule works because each digit is now worth ten times its original value.
basic multiplication
Understanding basic multiplication is essential. Multiplication is like adding a number to itself multiple times. For example, multiplying 4 by 3 means you add 4, three times: 4 + 4 + 4 = 12.
When multiplying by 10, this can be visualized as adding a zero to the end of the number (for whole numbers), or moving the decimal point for numbers with decimals. Multiplying 12 by 10 gives us 120. For numbers with decimals, such as 123.26, multiplying by 10 shifts each digit one place to the right, resulting in 1232.6.
This concept relies on understanding the position of digits and their value. Each move to the right increases the value of each digit by a factor of 10.
understanding operations
Operations like multiplication and division follow certain rules that simplify calculations. In our example, we are multiplying by 10, which involves moving the decimal point.
It's important to understand why these rules exist. Multiplication makes a number larger, adding groups of a number together. Similarly, multiplying by a power of 10, such as 10, 100, or 1000, shifts the decimal point to make it easier. Each 10 moves the decimal one place to the right.
  • A single 10 moves once.
  • One hundred (10 * 10) moves twice.
  • One thousand (10 * 10 * 10) moves thrice.
Understanding these operations is key to mastering basic arithmetic and handling more complex problems with ease.

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