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Understanding Percentages: Converting Between Decimal and Percentage for Accurate Calculations

This tutorial provides a comprehensive guide on calculating percentages and converting between decimal and percentage forms. It explains fundamental principles, such as understanding that "per cent" means "per hundred" and how to move the decimal point accordingly. Practical examples illustrate how to convert percentages to decimals and vice versa, calculate percentage changes, and apply these skills in real-world scenarios, like population changes or price adjustments. Engage with practice problems to solidify your understanding.

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Understanding Percentages: Converting Between Decimal and Percentage for Accurate Calculations

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Presentation Transcript

  1. Your Personal Tutor in Statistics Click for Next Calculating Areas Under the Normal Curve Percentage Calculations

  2. For example, 50% is the same as 1/2. Click for Next Click for Next Click for Next Calculating Percentages We are all familiar with certain percentages. Why? The word “per/cent” means “per hundred.” So 50% = 50/100 which equals 0.50, so 50% also equals 0.50. Don’t believe me? Put it in your calculator. Go ahead. OK, so 50% and 0.50 are exactly the same. Likewise, 38% and 0.38 are exactly the same. Going from % to decimal moves the decimal point 2 places to the LEFT. So…What is 55% as a decimal? = 0.55 . 55% = 55.% The leading zero is just a safety precaution to indicate that you just didn’t forget the leading digit.

  3. Click for Next Calculating Percentages So remember it this way… DECIMAL PERCENT 0.34 34 % Move decimal 2 places to right DECIMAL PERCENT 0.34 34 % Move decimal 2 places to left

  4. Click for Next Calculating Percentages Now to practice. Answer the question then click to see the answer. Convert 45% to decimal. 0.45 Convert 38.34% to decimal. 0.3834 Convert 0.005% to decimal. 0.00005 Convert 238.1% to decimal. 02.381 Let’s continue. Convert 0.45 to percent. 45% Convert 7.574 to percent. 757.4% Convert 0.005 to percent. 0.5% Convert .3875 to percent. 38.75%

  5. Click for Next Click for Next Click for Next Calculating Percentages Using Percentages To take the percent of a number, convert the percent to a decimal and multiply. For example, A city with a population of 3.8 million people grew by 3.65%. How many people were added? Convert to decimal, 3.65% 0.0365 0.0365 x 3.8 = .1387 million people In another city the population decreased by 4%. If the initial population was 2.6 million, what was the population after the decrease? There is more than one way to do this problem. 1. You could convert 4% to decimal 0.04 and then multiply 0.04 x 2.6 = 0.104 million. Then the population is 2.6 – 0.104 = 2.496 . . . or . . . 2. If the population decreased by 4%, then it will become 96% of what it was initially. So 96% of 2.6 million is 0.96 x 2.6 = 2.496 million Ready to do some more problems?

  6. Click for Next Calculating Percentages Using Percentages Now we will explore how percentages are used. Percentages are a way of comparing two numbers. For example, $50 $40 If a $50 item is reduced by $10, what is the percent change? The question really asks, “what was the change compared to the original price?” The change was -10 = -0.20 = -20% The original price was 50 So we have a change of -20%. If the price had gone up to $65, what would the percent change have been? The change is now 15 = 0.30 = 30% The original price was 50 So we have a change of 30%.

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