Question

Multiply the following numbers by moving the decimal. \(0.002 \times 100=\) ______

Short answer

0.2

Step-by-step solution

Identify the Operation

The exercise involves multiplying the decimal number 0.002 by 100. Our goal is to move the decimal point in the number 0.002 to the right to simplify this multiplication.

Determine Decimal Movement

To multiply a number by 100, move the decimal point two places to the right. This is because 100 has two zeros, indicating two decimal places.

Move the Decimal Point

Starting with 0.002, move the decimal point two places to the right: 1. Move once: 0.02 2. Move again: 0.2 Thus, 0.002 becomes 0.2.

Verify the Calculation

Double-check the movement of the decimal to ensure accuracy. Initially: 0.002 After moving two places: 0.2 This verifies that the calculation was done correctly.

Key concepts

Decimal Point Movement

When multiplying decimal numbers, a simple yet powerful trick is called decimal point movement. This concept is about understanding how shifting the decimal point modifies the value of a number. For instance, in the exercise, you multiply 0.002 by 100. Instead of doing lengthy multiplication, you simply move the decimal point.

• In the case of 0.002, moving the decimal two places to the right changes the number to 0.2.
• Each shift to the right by one position increases the number’s value tenfold.

Mastering decimal point movement simplifies many arithmetic problems, especially in fractions and decimals.

Multiplication by Powers of Ten

Multiplying by powers of ten is an important arithmetic technique. It is based on the number of zeros in the power of ten, indicating how many places you should move the decimal point. In our example, multiplying 0.002 by 100 involves shifting the decimal point rightwards.

• The number 100 has two zeros, hence you move the decimal two places.
• For example, if it were 1000, you would move it three places.

This method is quick and eliminates the need for traditional multiplication, thus saving time and reducing potential errors.

Basic Arithmetic Operations

Understanding basic arithmetic operations, such as multiplication, enhances your math skills. In the problem above, multiplication and decimal shifts work together for a solution. This combines simple operations with decimal rules.

• Such problems reinforce core skills in handling digits and places, crucial for more complex mathematics.
• Multiplying decimals by whole numbers is a fundamental skill needed for learning about percentages and financial calculations.

By mastering basic operations, you build a strong foundation for tackling advanced mathematical problems.