91Ó°ÊÓ

When you multiply decimals, you are essentially finding the product of two numbers that include decimal points. Begin by ignoring the decimals and multiply the numbers as if they were whole numbers. For example, if we multiply 0.05 by 1.2:

First, forget the decimal points:
\(0.05 \times 1.2 = 5 \times 12 = 60\)

Next, count the total number of digits to the right of the decimal points in both of the original numbers. In this case, 0.05 has two digits and 1.2 has one digit for a total of three digits:
\(5 (.00) \rightarrow \text{two decimal places} \) \(12 (.0) \rightarrow \text{one decimal place} \)

Finally, place the decimal point in the product so that it has the same number of decimal places:
\(60 \rightarrow . . 60 \rightarrow 0.060 \text{ (3 decimal places)} \)

Therefore, \( 0.05 \times 1.2 = 0.060 \)
And \( 0.05 \times -1.2 = -0.060 \)

Negative numbers are numbers less than zero. They are represented with a minus sign (-) before the number. Understanding how they interact in multiplication is important:

• When you multiply a positive number by a negative number, the result is a negative number. For example: \( 4 \times -3 = -12 \)
• When you multiply two negative numbers, the result is a positive number. For instance: \( -2 \times -3 = 6 \)

In this exercise:
\( (0.05) \times (-1.2) = -0.06 \)
Here, one number is positive (0.05) and the other is negative (-1.2). Therefore, the product is negative: \( -0.06 \)

The final goal is to express the multiplication result in its simplest form. Simplifying an expression means reducing it to its most basic form without changing its value:

In this case, \(0.05 \times -1.2 = -0.06 \) is already simplified because:

• The multiplication has been properly carried out.
• We have not introduced any unnecessary complexity or extra steps.
• Negative exponents are avoided since the given problem specifies not to use them.

When simplifying for decimals, ensure you have correctly placed the decimal point and simplified the number as much as possible without altering its value. For example, \( 0.060 \rightarrow 0.06 \)

Finally, \( 0.05 \times -1.2 = -0.06 \) remains the simplified form of the given expression.