Problem 53 - Prealgebra

Question

What does multiplying a decimal number by 100 do to the decimal point?

Step-by-Step Solution

Answer

Multiplying a decimal by 100 shifts the decimal point two places to the right.

Step 1: Understanding the Basics

When a decimal number is written, its position relative to the decimal point determines its value. Multiplying by 10 shifts the decimal point one place to the right, effectively increasing the value tenfold.

Step 2: Applying the Rule to 100

Since multiplying by 100 is the same as multiplying by 10 twice (100 = 10 x 10), it means we need to shift the decimal point two places to the right.

Step 3: Illustrating with an Example

Consider the decimal number 3.47. Initially, the decimal point is after the first digit: 3.47. When we multiply this number by 100, we move the decimal point two places to the right, resulting in 347.

Key Concepts

Multiplying Decimals

When multiplying decimals, it's important to treat them like whole numbers first, ignoring the decimal point. Once you've done the basic multiplication, count the total number of digits to the right of the decimal points in the numbers you are multiplying. This count will help you determine where to place the decimal point in the answer.
For instance, if you are multiplying 3.47 by 100, consider 347 without the decimal point. Multiply it by 100, and you get 34700. Then, count the decimal places in the original number 3.47, which has two decimal places.
Add these places back into your result, and since multiplying by 100 already shifts the decimal two places to the right, the result is 34700 without needing to adjust the decimal further.

Decimal Point Shift

The decimal point shift is a crucial part of understanding operations with decimals. Whenever you multiply a decimal by a power of 10, you shift the decimal point to the right. The number of places you move depends on the power of 10 you are using.

• When multiplying by 10, shift one place to the right.
• When multiplying by 100, shift two places to the right.
• Continue adding one shift for every power of ten you multiply by.

For example, multiplying 4.25 by 100 requires moving the decimal point two places to the right, transforming it to 425.0. Remember, this shift doesn't change the number of significant figures; it only impacts the position of the decimal and, thus, the scale of the number.

Place Value

Place value denotes the position of a digit in a number, indicating its value. For decimal numbers, each move to the right from the decimal point signifies a decrease in place value by a factor of ten.
When you multiply a number by 100, like 3.47, the decimal point's shift increases each digit's place value. The number 3.47 has its digits in the ones, tenths, and hundredths places, respectively. After multiplying by 100, the digits are now in the hundreds, tens, and units places.

• The digit '3' moves from the ones to the hundreds place.
• '4' moves from the tenths to the tens place.
• '7' moves from the hundredths to the units place.

Understanding place value helps in seeing how multiplication affects the scale and size of numbers.