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Percentage as fraction or decimals

Percentage as fraction or decimals

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Converting Between Percentages, Fractions, and Decimals

Did you know that percentages, fractions, and decimals are all related and can be converted into one another? In this article, we will explore the process of converting between these different forms and provide examples for better understanding.

The Relationship Between Equivalent Fractions, Decimals, and Percentages

Fractions, decimals, and percentages that have the same value are known as equivalent. This means that converting from one form to another will not change the value. For example, the fraction 1/2, the decimal 0.5, and the percentage 50% are all equivalent. This can be confirmed by converting from one form to another.

Converting Fractions to Percentages

To convert a fraction to a percentage, simply multiply it by 100%. This does not change the value but converts the form. It is important to remember that 100% is equivalent to 1. For instance, if we want to convert 1/2 to a percentage, we multiply by 100% and get 50%. Similarly, for 3/5, we multiply by 100% and get 60%.

Converting Percentages to Fractions

Converting percentages to fractions is also a simple process. Divide the percentage by 100% to get the equivalent fraction. For example, to convert 75% to a fraction, we divide 75% by 100% and get 3/4. Likewise, to convert 260% to a fraction, we divide 260% by 100% and get 13/5.

Converting Decimals to Percentages

The process of converting decimals to percentages involves multiplying the decimal by 100%. So, a decimal like 0.7 would become 70% and 1.6 would become 160%.

Converting Percentages to Decimals

To convert a percentage to a decimal, divide it by 100%. Keep in mind that this will result in a fraction, so you may need to convert the fraction to a decimal using the steps below.

For example, if we have 70%, dividing it by 100% would give us 0.7. Similarly, 160% would become 1.6.

Converting Decimals to Fractions

To convert a decimal to a fraction, follow these steps:

  • Count the number of decimal places (d.p) - this will determine the number of 0s in the denominator (e.g. 1 d.p would be 10, 2 d.p would be 100, etc.)
  • Remove the decimal point and divide the number by the corresponding power of 10.

For example, to convert 0.125 to a fraction, we would divide it by 1000 and get 125/1000. This fraction can be simplified to 1/8.

Let's take another example, 0.2. We divide it by 10 and get 2/10, which can be simplified to 1/5.

Converting Fractions to Decimals

The process of converting fractions to decimals is slightly different. To do this, we divide the numerator by the denominator. If the numerator is smaller than the denominator, we add a 0 in front of the numerator and continue dividing. For example, to convert 1/5 to a decimal, we divide 1 by 5 and get 0 with a remainder of 1. Then, we add a 0 in front of the 1 and continue dividing. 10 divided by 5 is 2 with no remainder, so our final answer is 0.2. Likewise, to convert 3/4 to a decimal, we divide 3 by 4 and get 0 with a remainder of 3. We add a 0 in front of the 3 and continue dividing. 30 divided by 4 is 7 with a remainder of 2. We add another 0 and continue dividing. 20 divided by 4 is 5 with no remainder, so our final answer is 0.75.

Now that we have a better understanding of how to convert between percentages, fractions, and decimals, we can easily solve any conversion problems we may encounter.

Decimals and fractions are often difficult to understand and convert for students. However, this guide will simplify the process and make it easier for you to convert between the two. Read on to learn the steps to convert decimals to fractions and gain a clear understanding of this process.

  • Step 1: Identify the number of decimal places

The first step in converting decimals to fractions is to identify the number of decimal places in the given decimal.

  • Step 2: Count the number of decimal places

Once you have identified the number of decimal places, count the number of digits after the decimal point. This will determine the denominator of the fraction. For example, 0.25 has two decimal places, so the denominator will be 100.

Similarly, if the decimal has three places, the denominator will be 1000 and so on. This step is crucial as it helps determine the accuracy of the final fraction.

  • Step 3: Eliminate the decimal

Next, eliminate the decimal point by multiplying the decimal by 10 or 100, depending on the number of decimal places. This will move the decimal point to the right, making the number a whole number. For example, if the decimal is 0.25, multiply it by 100 to get 25.

Remember, whatever you do to the decimal, you must do to the numerator as well. So, in this case, 0.25 becomes 25/100.

  • Step 4: Simplify the fraction

The final step is to simplify the fraction. Divide both the numerator and denominator by the greatest common factor (GCF) to get the simplified fraction. In this case, the GCF of 25 and 100 is 25. Dividing both by 25 gives us the final fraction, which is 1/4.

By following these steps, converting a decimal to a fraction is a straightforward process. Now, let's look at converting fractions to decimals using the same approach.

Converting Fractions to Decimals

The process of converting fractions to decimals follows a similar method. Let's take the example of 1/8. To convert this fraction to a decimal, divide 1 by 8, resulting in 0.125.

Another way to approach this is to place a zero and a decimal point after the one, making it 10 divided by 8, which equals 1 with a remainder of 2. This remainder is then placed on top of 10, and we continue the process of dividing until there is no remainder left. In this case, the final result is 0.125.

A similar approach can be used for converting decimals to fractions. For example, the decimal 0.5 can be written as 5/10, which can then be simplified to 1/2. Similarly, percentages can also be expressed as decimals by dividing the percentage by 100%. So, 25% would equal 0.25 as a decimal.

Applying Long Division for Conversion

Another method for converting fractions to decimals is using long division. This involves using the long division sign and rule to simplify the process. Let's apply this method to the previous examples.

  • a) Converting 1/5 to a decimal:

Divide 1 by 5, resulting in 0.2.

  • b) Converting 1/8 to a decimal:

Divide 1 by 8, resulting in 0.125.

Similarly, we can apply long division to convert decimals to fractions and percentages as well.

Further Examples

Let's explore more examples to better understand the conversion of percentages to fractions and decimals.

If a man on a project has completed 15% of the task, we can determine the fraction left and the fraction remaining if the total task was reduced by 30%.

  • a) What fraction is left?

The fraction left would be 85/100 or 17/20.

  • b) What fraction of the new volume expressed in decimal would he have left to do?

The new volume would be 70/100 or 7/10. Converting this to a decimal would result in 0.7.

Equivalent Fractions, Decimals, and Percentages

In order to fully understand conversions, it is important to know about equivalent fractions, decimals, and percentages. These are values that are of the same value regardless of how they are expressed. For example, 0.33, 33.3%, and are all equivalent.

When looking at a table with fractions, decimals, and percentages, you can determine if they are equivalent by simplifying them. For example, the set , 0.33, and 33.3% are all equivalent because they all simplify to 1/3.

On the other hand, the set , 0.3, and 32% are not equivalent because they do not simplify to the same value. However, the fraction and 40% are equivalent, but the decimal 0.2 is not equivalent to them.

Summary

In summary, understanding the conversion of fractions to decimals and percentages, and vice versa, is important in solving mathematical problems. It involves dividing and multiplying by 100% and using the long division method for larger fractions. Knowing equivalent values can also help in simplifying fractions, decimals, and percentages. With these tools, you can confidently convert between these different forms and express your answers in the most appropriate format.

References:

  • How to convert fractions to decimals and percentages, Math is Fun, https://www.mathsisfun.com/converting-fractions-percents.html
  • Converting fractions, decimals, and percents, Khan Academy,https://www.khanacademy.org/math/pre-algebra/pre-algebra-fractions-pre-alg/percent-as-decimal-pre-alg/a/converting-between-fractions-decimals-and-percents-review

Additional Resources:

  • Percentage as fractions and decimals, StudyPug, https://www.studypug.com/percents-as-fractions-and-decimals
  • How to Convert Fractions Into Decimals, The Balance, https://www.thebalance.com/calculate-fractions-and-decimals-3126506
  • How to Convert a Percentage to a Decimal, WikiHow, https://www.wikihow.com/Convert-a-Percentage-to-a-Decimal

Converting Decimals to Fractions: A Simple Guide

When working with decimals, it can be useful to convert them to fractions for easier calculation and comparison. This process involves identifying the number of decimal places, removing the decimal point, and determining the denominator of the fraction. Here's a step-by-step guide to make this conversion method a breeze.

  • Step 1: Identify the number of decimal places

The first step is to count the number of decimal places in the given number. This will help in determining the denominator of the fraction.

  • Step 2: Remove the decimal point

Once the number of decimal places is identified, the decimal point is removed from the number. The resulting number without the decimal point will serve as the numerator of the fraction.

  • Step 3: Determine the denominator

The denominator of the fraction is determined by the number of decimal places. For every decimal place, the decimal point is moved one place to the right, and a 1 is placed in the numerator. For example, for two decimal places, the denominator would be 100.

  • Step 4: Simplify the fraction (optional)

If the numerator and denominator have a common factor, they can be simplified to their lowest terms. While this step is optional, it can make the fraction easier to work with.

Now, let's go through an example to better understand the process. Say we have the number 3.25 and want to convert it to a fraction.

  • Step 1: The number 3.25 has two decimal places.
  • Step 2: Removing the decimal point, we get 325 as the numerator.
  • Step 3: For two decimal places, we move the decimal point two places to the right, making the denominator 100. So the fraction is 325/100.
  • Step 4: Since both the numerator and denominator are divisible by 25, we can simplify the fraction to 13/4.

By following these simple steps, converting decimals to fractions becomes a straightforward process. Remember to identify the number of decimal places, remove the decimal point, and determine the denominator. With practice, anyone can quickly master this conversion method and make mathematics a little less daunting.

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