Problem 287 - Intermediate Algebra

Question

In the following exercises, convert each decimal to a percent. $$ 1.56 $$

Step-by-Step Solution

Answer

156%

Step 1: Understand the Problem

The task is to convert the decimal number 1.56 to a percent. A percent represents a number out of 100.

Step 2: Multiply by 100

To convert a decimal to a percent, multiply the decimal number by 100. This means you need to calculate 1.56 * 100.

Step 3: Perform the Multiplication

Calculate the product of 1.56 and 100: 1.56 * 100 = 156

Step 4: Write the Result

After multiplying, write the result followed by the percent sign (%). So, 1.56 * 100 = 156%, hence the percent form of 1.56 is 156%.

Key Concepts

Percent Conversion

When you convert a decimal to a percent, you're essentially working out what that decimal would be if it were out of 100. This is useful in many real-world applications, like calculating discounts or interest rates. For example, if you have a decimal like 0.75, you want to see this as a value out of 100. The basic rule here is to multiply the decimal by 100 to get its percent equivalent.

So in our exercise, converting 1.56 to a percent means performing the multiplication: \(1.56 * 100\). The result is 156, which we then write as 156%. Remember, this works because moving the decimal point two places to the right translates the decimal into its percentage form.

Decimal Multiplication

Decimal multiplication is a fundamental arithmetic skill that helps us understand more complex math problems down the road. To multiply decimals, simply multiply as if there are no decimal points, and then count the total number of decimal places in both original numbers to place the decimal correctly in the final answer.

In our example, multiplying 1.56 by 100 is straightforward.
1.56 has two decimal places; 100 has none. Thus, you simply multiply normally: \(1.56 * 100 = 156\). Since 100 is a whole number, you can perform this multiplication directly, without needing to adjust for additional decimal places in the product.

Basic Arithmetic Operations

Understanding basic arithmetic operations like addition, subtraction, multiplication, and division is essential. These operations form the backbone of more complicated math problems.
In our exercise, we specifically use multiplication. To multiply any two numbers, follow these steps:

• Write down the numbers aligned vertically, starting from the right.
• Multiply each digit of the bottom number with each digit of the top number, one at a time.
• Add up all the resulting products, taking care to place each number in the correct position based on place value.

For 1.56 and 100, we need to multiply normally: \(1.56 * 100\). Starting from the rightmost digit, we perform the multiplication as shown in our solution.