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Chapter 7: Problem 44

Convert the given decimal to a percent. $$ 8.78 $$

Short Answer

Expert verified
878%

Step by step solution

01

Understand the Conversion

To convert a decimal to a percentage, you need to multiply the decimal by 100, as a percentage signifies the number per hundred. This process will shift the decimal point two places to the right.
02

Multiply the Decimal by 100

Take the given decimal, which is 8.78, and multiply it by 100.\[8.78 \times 100 = 878\]
03

Add the Percent Sign

The result from Step 2 is the number expressed per hundred, so we denote it with a percent sign (%). Therefore, the percentage form of the decimal 8.78 is 878%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Multiplying Decimals
Multiplying decimals involves a process similar to multiplying whole numbers, but with attention to the placement of the decimal point. When you multiply a decimal by 100, you simply move the decimal point two places to the right.
  • Start by visualizing how regular multiplication works without considering the decimal points. For instance, understanding how to multiply 878 by 1 can help.
  • Once the basic multiplication is performed, adjust the product by placing the decimal point in the correct position, but for multiplying by 100, you don't need to worry about this as it is a straightforward shift of the decimal point.
This shifting of the decimal point when multiplying by 100 is crucial and makes the calculation very simple and efficient.
Percentage Calculation
Calculating a percentage from any decimal involves a simple process. Here鈥檚 how:
  • Understand that a percentage is essentially the value per 100 units. Thus, converting a decimal to a percentage tells you how many parts out of 100 your decimal represents.
  • To find out the percentage of a number represented by a decimal, multiply the decimal value by 100 (e.g., for a decimal of 8.78, this multiplication gives 878).
  • Add a percentage sign (%) to denote the computed value is a percentage, such as concluding the conversion of 8.78 to 878%.
This method accurately converts any decimal to a percentage, making it easier to understand large or small figures in a context that is familiar.
Decimal Point Movement
Moving the decimal point is an essential skill in calculating percentages and multiplying decimals. When you multiply a decimal by powers of ten, the decimal point moves to the right.
  • Multiplying by 10 moves the decimal point one place to the right.
  • Multiplying by 100 shifts it two places to the right, which is exactly what we do when converting decimals to percentages.
  • Similarly, multiplying by 1,000 would move it three places, and so on.
Knowing the number of spaces to move the decimal is key to correctly adjusting the value. This movement helps in understanding not just percentages, but also in scaling numbers effortlessly in different mathematical scenarios.

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