Percentage and Decimal Review - Online Tutor, Practice Problems & Exam Prep

Understanding the conversion between percentages and decimals is crucial. To convert a percentage to a decimal, move the decimal point two places to the left; for example, 50% becomes 0.50. Conversely, to convert a decimal to a percentage, move the decimal point two places to the right, such as 0.34 becoming 34%. Additionally, calculating percentage change involves the formula: $(\mathrm{new}-\mathrm{original})/\mathrm{original}$. For instance, a change from 550,000 to 800,000 results in a percentage change of 45.45%.

Converting Percentages and Decimals

So now let's do a quick review of percentages and decimals. The first thing we want to be able to do is switch between percentages and decimals. Take a percentage and turn it into a decimal, or a decimal and turn it into a percentage. In both cases, the idea is we have to identify where the decimal point is, and a lot of times that's easy if you have a number like 150.23, but what if you just had the number 16? In this situation, the decimal point is implied at the end here. So if you don't see one, it's going to be at the end, and when we're going from percentage to decimal, we're going to move the decimal point 2 spaces to the left, and when we're going from decimal to percentage, we're going to move 2 places to the right. Cool?

So let's go ahead and practice a little bit. I'm just going to keep this in the same video for this practice. What I want you to do is, why don't you pause the video real quick, do these, and then continue, and we'll go through them together. So I'm guessing you paused the video and you're back now. Let's do this:

• 50% converts to a decimal of 0.50 or 0.5. You can drop that last zero and it's okay.
• 1.25% moves 2 places to the left, and now our new decimal here, we have to add a zero in there, and we're going to get 0.0125 for 1.25%.
• For 120%, we've got our decimal point right there, move 2 to the left and we're going to get 1.2 is equal to 120%.
• For 5%, we're going to move it 1 space, 2 spaces, fill it with a zero, and we are going to get 0.05 for that one.
• For 31.34%, we're just going to move the decimal two to the left and get 0.3134.
• 12.5% moves 2 to the left to point 0.125.
• For 0.5%, notice comparing this to 5% and 50%. We're going to move it 1, 2 spaces, add a zero in there, and we're going to get 0.005 is 0.5%.
• For 100%, move it 2, and we're going to get 1 is the answer there. Just 1.

Let's do the same thing here with the decimals to percentage on the bottom.

So you're back now. Let's go ahead and solve these:

• For 0.34, we are going to move 2 to the right to become a percentage, and we're going to get 34% for this first one.
• For 0.61, move 2, and you're going to get 61%.
• For 0.06, move 2, and we are going to get 6%.
• For 0.4512, move 2, and we'll get 45.12%.
• For 0.0004, we're also going to move it over 2 and we are going to get a decimal of 0.04. You could also write 0.04%, right.
• The last one, the number 1. Remember if it doesn't give us the decimal, it's implied at the end. So we're going to move it 1, 2, add the zeros, and we'll get 100% for 1.

So that is converting percentages and decimals. Let's move on to the next video.

Calculating Percentage Change

Alright, so now let's review how to calculate percentage change. This is the amount that something has changed in percent. If we started at 10 and now we are at 15, what is the percentage change from 10 to 15? This is going to be the formula that we use. The percentage change equals

change in x original value of x ,

where x is whatever we're trying to find the percentage change of. Another way to think of the change in x is it's the new value for x minus the original value for x. We're going to divide that by the original value. Let's try this first example:

Last year's sales revenue totaled 550,000. Current year, excuse me, current year sales revenue increased to 800,000. Calculate the percentage change in sales revenue. Alright, we're going to use this formula, and we are going to calculate the percentage change equals

change in x original value ,

So, the current year sales increased to 800,000. This is our new value, and this is our original last year's value. Let's calculate this percentage change. Our new value being 800,000 minus 550,000 divided by our original value which was 550,000. So we get

250,000 550,000

and let's see what we get there. Our answer is going to be 0.4545. But is this answer in a decimal or a percentage? It gives it to us as a decimal. Let's convert it to a percentage. We're going to take our decimal and move it two places to the right, and it's going to end up being 45.45 percent. Cool?

Alright. So in the next video, you guys are going to practice this next one here.

The price of Clutch Pizza was originally $12. Clutch decides that everyone deserves more pizza and lowers the price to $10. Calculate the percentage change in the price of Clutch Pizza.

Alright. So let's go ahead and do this practice problem in the middle of the page. The price of Clutch Pizza was originally $12. Clutch decides that everyone deserves more pizza and lowers the price to $10. Man, they're good to us. Calculate the percentage change in the price of Clutch pizza. Alright. So let's go ahead and use our same formula. The percentage change is going to be equal to the new value minus the old value divided by the old value. So in this case, what is our new value? What's our old value? Well, we've got our new price of $10 and our old price of $12. So let's plug those in here. We've got: new 10 − 12 divided by 12 , right, and let's do the numerator. We've got: 10 − 12 = − 2 over 12 right? So this will result in a negative number: −2 12 and when we do that division, we get: −2 12 which equals: −0.16667. Those sixes go on forever. I'm gonna get out of the way here. So it's −0.166666-666, but we'll just cut it off there, −0.1667. So, we gotta convert this to a percentage, and we're going to move the decimal two places to the right, and we are going to get a final answer, a percentage change of −16.67%. So the price went down 16.67% there. Alright? Cool. Let's move on.

Here’s what students ask on this topic:

How do you convert a percentage to a decimal?

To convert a percentage to a decimal, you need to move the decimal point two places to the left. For example, if you have 50%, you move the decimal point two places to the left, resulting in 0.50. This is because percentages are essentially fractions out of 100, so moving the decimal point two places to the left divides the number by 100.

How do you convert a decimal to a percentage?

To convert a decimal to a percentage, you move the decimal point two places to the right. For instance, if you have 0.34, moving the decimal point two places to the right gives you 34%. This is because you are essentially multiplying the decimal by 100 to convert it into a percentage.

What is the formula for calculating percentage change?

The formula for calculating percentage change is: $\frac{(\mathrm{new}-\mathrm{original})}{\mathrm{original}}$. This formula calculates the change in value as a fraction of the original value. To express this as a percentage, multiply the result by 100.

How do you calculate the percentage change from 550,000 to 800,000?

To calculate the percentage change from 550,000 to 800,000, use the formula: $\frac{(800000-550000)}{550000}$. This gives you $\frac{250000}{550000}$, which equals approximately 0.4545. To convert this to a percentage, move the decimal point two places to the right, resulting in 45.45%.

What is the difference between 5% and 50% in decimal form?

The difference between 5% and 50% in decimal form is significant. To convert 5% to a decimal, move the decimal point two places to the left, resulting in 0.05. For 50%, do the same, resulting in 0.50. Notice that 0.05 is much smaller than 0.50, reflecting the difference in magnitude between 5% and 50%.