Question

Multiply the following numbers by moving the decimal. \(5.65 \times 100=\) ______

Short answer

565

Step-by-step solution

Identify the Decimal Movement

When multiplying a number by 100, the decimal point is shifted two places to the right.

Apply Decimal Movement to 5.65

Starting with 5.65, we move the decimal point two places to the right. This transforms 5.65 into 565.0.

Simplify the Result

The number 565.0 is equivalent to 565 when expressed without the decimal point. Thus, the result of the multiplication is 565.

Key concepts

Decimal Movement

Decimal movement is a crucial concept when multiplying decimals by powers of 10, such as 10, 100, 1000, and so on. This process is straightforward:

• When multiplying by 10, shift the decimal point one place to the right.
• When multiplying by 100, move the decimal two places to the right.
• When multiplying by 1000, move it three places to the right.

As demonstrated in our example, multiplying 5.65 by 100 involves a two-place right shift in the decimal. After the shift, the number becomes 565.0. By removing the decimal, we simplify it to 565. This illustrates how simple multiplication can be made by grasping decimal movement.

Multiplication Steps

Understanding the steps involved in decimal multiplication is vital to mastering this operation.
Let's break it down using our example, 5.65 multiplied by 100:

• Step 1: Identify the decimal placement. You know that multiplying by 100 moves the decimal two places to the right.
• Step 2: Physically shift the decimal. In 5.65, move the point right twice to get 565.0.
• Step 3: Simplify the answer. Strip away any unnecessary decimal points resulting in a whole number, which in this case is 565.

These steps make decimal multiplication not only manageable but also intuitive once practiced repeatedly.

Place Value

Place value is the foundation that supports all decimal arithmetic, including multiplication. It refers to the position of each digit in a number, which determines its actual value.
Consider 5.65:

• The 5 is located in the units place (ones), making it 5.
• After the decimal, 6 is in the tenths place, which assigns it a value of 0.6.
• The 5 at the end is in the hundredths place, worth 0.05.

By multiplying by 100, we shift each digit two places to the right, without changing their respective order but altering their place value.
This way, understanding place value helps accurately reposition decimals, ensuring multiplication is done correctly.