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

To calculate percentage change, use the formula: $(\mathrm{New\; Value}-\mathrm{Original\; Value})/\mathrm{Original\; Value}$. For example, if sales revenue increased from $550,000 to $800,000, the change is $250,000. Dividing this by the original value gives 0.45, which converts to 45% when moved two decimal places to the right. Understanding percentage change is crucial for analyzing economic trends and market performance.

Calculating Percentage Change

Alright, so now let's review how to calculate percentage change. This is the amount that something has changed in percent. So 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.

So, it's going to be the change in x over the original value of x, x being whatever we're trying to find the percentage change of, right? Another way to think of the change in x is the new value for x minus the original value for x, right? And we're going to divide that by the original value.

So let's try this first example here. We've got 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, so we're going to use this formula and we are going to do the percentage change equals Δxx, so how do we calculate the change in x? It tells us that the current year sales increased to 800,000. So this is our new value here and this is our original, last year's value. So let's calculate this percentage change.

Our new value being 800,000 I'm going to put 800Ks here for 1,000 minus 550,000 or 550Ks divided by our original value which was 550Ks. Alright, so we get 800 minus 550 is going to be 250Ks over 550K, and let's see what we get there. Our answer is going to be 0.4545. Alright.

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. What we're going to do is take our decimal and move it 2 places to the right. So, move it 2 places to the right, and it's going to end up as 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 on 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. Percentage change is going to be equal to, let's just say, new minus old divided by old, right? So 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 10-12÷12, right, and let's do the numerator. We've got 10-12=-2 over 12, right? So we've got a negative number here and when we do that division, -212, and we get -0.16667. Those sixes go on forever. I'm gonna get out of the way here. So it's -0.16 6666-666, but we'll just cut it off there, -0.16667. So we've got to convert this to a percentage, and we're going to move the decimal two places to the right, and we're 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 calculate percentage change?

To calculate percentage change, use the formula: $\frac{(\mathrm{New\; Value}-\mathrm{Original\; Value})}{\mathrm{Original\; Value}}$. For example, if sales revenue increased from $550,000 to $800,000, the change is $250,000. Dividing this by the original value gives 0.45, which converts to 45% when moved two decimal places to the right. Understanding percentage change is crucial for analyzing economic trends and market performance.

What is the formula for percentage change?

The formula for percentage change is: $\frac{(\mathrm{New\; Value}-\mathrm{Original\; Value})}{\mathrm{Original\; Value}}$. This formula helps you determine the relative change between two values, expressed as a percentage. For instance, if the original value is 10 and the new value is 15, the percentage change is $\frac{(15-10)}{10}$ = 0.5 or 50%.

How do you convert a decimal to a percentage?

To convert a decimal to a percentage, move the decimal point two places to the right and add a percentage sign (%). For example, if you have a decimal value of 0.45, moving the decimal two places to the right gives you 45. Therefore, 0.45 as a percentage is 45%.

What is the percentage change if sales revenue increased from $550,000 to $800,000?

To find the percentage change, use the formula: $\frac{(\mathrm{800,000}-\mathrm{550,000})}{\mathrm{550,000}}$. The change is $250,000. Dividing this by the original value of $550,000 gives approximately 0.4545. Converting this decimal to a percentage by moving the decimal point two places to the right gives 45.45%. Therefore, the percentage change is 45.45%.

Why is understanding percentage change important in economics?

Understanding percentage change is crucial in economics because it allows analysts to measure the relative change in economic variables over time. This helps in comparing different periods, assessing growth rates, and making informed decisions. For example, knowing the percentage change in sales revenue can help businesses evaluate their performance and strategize for future growth.