Problem 77 - Algebra A Combined Function

Question

Write each decimal as a percent. $$ 1 $$

Step-by-Step Solution

Answer

1 as a percent is 100%.

Step 1: Understand the Problem

The exercise requires us to convert the decimal number 1 into a percentage. Knowing that percentages are another way of expressing a number relative to 100, we should start by identifying the decimal value, which is a straightforward 1 in this case.

Step 2: Multiply by 100

To convert a decimal to a percentage, multiply the decimal by 100. Thus, we compute: \[ 1 \times 100 \]

Step 3: Perform the Multiplication

Perform the multiplication from Step 2:\[ 1 \times 100 = 100 \] This calculation shows that the decimal 1 equals 100 when expressed as a percentage.

Key Concepts

Multiplying Decimals

When it comes to multiplying decimals, the process is somewhat similar to multiplying whole numbers. However, there are a few extra considerations to keep in mind. By understanding these key points, you can successfully work through any problem involving decimal multiplication.

First, ignore the decimal points and multiply the numbers as if they are whole numbers. In our case, multiplying decimal 1 by 100 simplifies to multiplying 1 by 100. Since there are no decimal places in the number 1, this multiplication remains straightforward.

• Multiply the numbers as whole numbers.
• Reintroduce the decimal point to the product (though in this case there's no need).

After multiplying, make sure to reinsert the decimal point in the final product. Since in our specific problem (1 times 100) does not originally contain decimal points beyond whole numbers, the translated answer remains 100.

In other scenarios, remember to count the total number of decimal places in the original numbers, and position the decimal point in the product accordingly. This ensures precise and correct results.

Expressing Numbers as Percentages

Transforming numbers into percentages is like presenting them in a form that compares them with 100. Percent literally means 'per hundred,' which simplifies understanding ratios and comparisons.

To convert any decimal to a percentage, multiply it by 100. Essentially, you're scaling up the number to see how many parts of 100 it represents. In our exercise, we were given the decimal 1. By multiplying it by 100, we find the percentage:

• Decimal = 1
• Percentage = 1 x 100 = 100%

This method transforms the decimal 1 into 100%, expressing it as a full whole in the context of 100.

In other cases like 0.75 as a decimal would become 75% after the conversion (0.75 × 100 = 75%). It's a straightforward way of looking at how a part or portion relates to the entirety of 100 parts.

Basic Arithmetic Operations

Understanding basic arithmetic operations like addition, subtraction, multiplication, and division forms the foundation of mathematics. Each operation serves a specific purpose and helps solve various mathematical problems.

In our context of converting decimals to percentages, multiplication plays a central role. Here's why it's significant:

• Addition - Not needed for conversion.
• Subtraction - Not needed here, though useful for comparisons in percentages.
• Multiplication - Key to conversion! Multiply by 100 to shift decimal to percentage form.
• Division - Helps find proportions and rates, although not required in this exercise.

In our specific example, multiplying the decimal 1 by 100 was the arithmetic step needed to convert it into a percentage.

Mastering these operations allows you to tackle various mathematical challenges, particularly those involving conversions and expressions amongst different numerical systems, like decimals and percentages.