Problem 68 - Elementary Algebra

Question

Convert the following decimals and fractions to percents. $$ 0.98 $$

Step-by-Step Solution

Answer

0.98 equals 98%.

Step 1: Understand the Concept

To convert a decimal to a percent, you need to multiply the decimal number by 100. This is because 'percent' means per hundred, so we are effectively finding how many hundredths the decimal represents.

Step 2: Multiply by 100

Take the decimal 0.98 and multiply it by 100. This will shift the decimal point two places to the right.

Step 3: Perform the Multiplication

Compute the product of 0.98 and 100: \[0.98 \times 100 = 98\]

Step 4: Add the Percent Sign

After obtaining the result from the multiplication, simply attach the percent sign to present it correctly as a percentage. This means the decimal 0.98 is equivalent to 98%.

Key Concepts

Decimal to Percent

Converting a decimal to a percent is a straightforward process, yet it's fundamental to understanding how values relate to each other on a scale of 100. When we say 'percent,' we refer to 'per hundred.' Therefore, converting a decimal to a percent involves scaling it as if it represents parts out of 100.

To perform this conversion, you simply need to multiply the decimal by 100. Let's break it down further:

• Take the decimal value you wish to convert. For example, consider the decimal 0.98.
• Multiply this decimal by 100: \[0.98 \times 100 = 98\]
• This multiplication shifts the decimal point two places to the right, giving us a whole number.
• Finally, attach a percent sign to your result, which in this case is 98%.

Remember, multiplying by 100 changes the scale, allowing the decimal to be expressed in terms of hundreds, which is precisely what a percentage is.

Multiplying Decimals

Understanding how to multiply decimals is key to numerous mathematical operations, including converting decimals to percentages.

When multiplying decimals, follow these straightforward steps:

• Ignore the decimal points initially and multiply the two numbers as if they were whole numbers.
• Once you have the multiplication product, count the total number of decimal places in both original numbers.
• Position the decimal in the product such that it has the same number of decimal places as the total counted in step 2.

For example, if you are multiplying 0.98 by 100:

• First treat 0.98 as 98 and 100 as 100, ignoring any decimals: \[98 \times 100 = 9800\]
• The original decimal, 0.98, has two decimal places. Therefore, position the decimal point two places from the right in the product 9800.
• This results in 98.00, which equals 98.

Understanding this process is crucial for accurate computation and conversion from decimals to percentages.

Understanding Percentages

Percentages are a versatile tool in mathematics that allow you to represent ratios and comparisons effectively. Grasping this concept helps in various fields such as finance, statistics, and daily life calculations.

A percentage signifies a number out of 100, simplifying the understanding of proportions. For example, when you see 98%, it means 98 out of 100. Here's how to grasp percentages fully:

• Percentages can describe how large or small one quantity is relative to another. They simplify the comparison process across different contexts.
• To calculate a percentage increase, subtract the old value from the new value, divide by the old value, and multiply by 100.
• To find the percentage of a number, multiply the number by the percentage (converted into a decimal). For example, calculating 25% of 200 involves converting 25% to 0.25 and multiplying: \[0.25 \times 200 = 50\]

Developing a strong understanding of percentages helps in making informed decisions in everyday scenarios such as shopping discounts, interest rates, and statistical data interpretation.