Problem 71 - Prealgebra

Question

Divide the decimal by the given power of 10 . \(\frac{694.55}{10}\)

Step-by-Step Solution

Answer

The result of dividing 694.55 by 10 is 69.455.

Step 1: Understand the Division by Power of 10

When dividing a number by a power of 10 like 10, 100, 1000, etc., you simply move the decimal point to the left by as many places as there are zeros in the power of 10. In this case, since 10 has one zero, we will move the decimal point one place to the left.

Step 2: Locate and Move the Decimal

The decimal number we are working with is 694.55. To divide by 10, move the decimal point one place to the left. Thus, the new position for the decimal point will be between 69 and 4.

Step 3: Write the Result

After moving the decimal point one place to the left, the number becomes 69.455. So, the result of dividing 694.55 by 10 is 69.455.

Key Concepts

Understanding the Decimal Point

The decimal point in a number plays a crucial role in determining its value. It separates the whole number part from the fractional part. For instance, in the number 694.55, the decimal point is positioned between "694" and "55," denoting that the number has 694 wholes and 55 hundredths.

When performing operations such as decimal division, we often need to shift this decimal point. This action directly influences the value of the number. Therefore, having a clear understanding of where the decimal point is before and after the operation is essential. In the case of dividing by 10, knowing that you move the decimal point one step to the left changes 694.55 to 69.455, which is the accurate result of this division.

The Power of Ten Concept

When we talk about a power of ten, we refer to numbers like 10, 100, or 1000. These numbers are also expressed as 10 raised to the power of 1, 2, or 3, respectively. The power tells us how many zeros follow the number 1. Therefore, 10 can be written as \(10^1\), 100 as \(10^2\), and 1000 as \(10^3\).

This concept is crucial in arithmetic operations, especially in decimal division. Each power of ten affects the decimal point's movement during division. This movement directly correlates with the number of zeros in the divisor. Remember, the power of ten reflects how significantly the number scales, whether we're reducing it in division or increasing it in multiplication.

Simple Division by 10

Division by 10 is among the simplest arithmetic operations one can perform, especially with decimals. The technique involves an effortless shift of the decimal point. Instead of complicated calculations, simply moving the decimal point one place to the left provides the correct result.

For example, dividing 694.55 by 10, requires moving the decimal from its current position to one digit leftward: thus changing it from 694.55 to 69.455. It's a straightforward process because there is only one zero in the number 10. This simplicity makes division by 10 an easy operation to accomplish quickly, without the need for long division. Such understanding reinforces basic math skills and offers a foundation for more complex mathematical concepts.