Problem 79 - Algebra 1: Concepts and Skills

Question

Multiply. $$ 0.1 \times 0.4 $$

Step-by-Step Solution

Answer

The result of the multiplication \(0.1 \times 0.4\) is \(0.04\).

Step 1: Multiply as if they were whole numbers

Ignore the decimal points for now and just multiply the numbers as if they were whole numbers. This would be: \(1 \times 4 = 4\).

Step 2: Count the total number of digits after decimal points in the original numbers.

Here, there is one digit after the decimal in 0.1 and one digit after the decimal in 0.4. So, the total is 2.

Step 3: Place the decimal point in the answer

Since there are 2 digits in total after the decimals in the original numbers, you need to place the decimal point 2 digits from the right in your answer. Hence, the final result is 0.04

Key Concepts

Multiplying Decimals

Multiplying decimals might seem confusing at first, but it's quite straightforward once you understand the process. The key is to first ignore the decimal points and treat the numbers like whole numbers. This helps you focus solely on multiplication. For example, if you're asked to multiply \(0.1\) by \(0.4\), you would initially set aside the decimals and multiply \(1\) by \(4\), which gives you \(4\).

Next, count all the digits that come after the decimal points in the numbers you were given. Both \(0.1\) and \(0.4\) have one digit after the decimal, adding up to two digits in total.

Finally, use this count to place your decimal in the result. In this case, you'll move the decimal point two places to the left in the product \(4\) to get \(0.04\). This systematic approach will help you multiply any decimals confidently.

Decimals in Math

Decimals are a way to represent fractions in a format that is easy to read and use, especially in calculations. They are based on the power of ten, which makes them very common and convenient in arithmetic.

Here's how decimals work in mathematics:

• The number to the left of the decimal point is the whole number part.
• The numbers to the right of the decimal point represent fractions of ten. For example, in the decimal \(0.4\), the \(4\) represents four-tenths.

Understanding how to work with decimals is crucial because they are used extensively in various fields, from finance to engineering. Practicing with simple operations like addition, subtraction, multiplication, and division will strengthen your grasp on using decimals effectively.

Elementary Algebra

Elementary Algebra forms the foundation for all higher math learning. It involves basic operations such as addition, subtraction, multiplication, and division, along with the use of variables and the formation of equations.

In algebra, understanding how to manipulate numbers and symbols is critical. Operations involving decimals, such as our earlier example, fit perfectly into elementary algebra learning. You apply the same rules and processes for solving equations and simplifying expressions, whether the numbers involved are whole or decimal.

The core idea is to solve for unknowns using these basic operations, making it essential to have a solid understanding of arithmetic, including decimals. Practicing algebraic techniques will enhance your problem-solving skills and prepare you for more advanced topics in mathematics.