7.2.1 - Estimation in percentages
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Interactive Audio Lesson
Listen to a student-teacher conversation explaining the topic in a relatable way.
Understanding Rounding
🔒 Unlock Audio Lesson
Sign up and enroll to listen to this audio lesson
Today we're going to learn how to estimate percentages, starting with rounding off numbers. Why do we round numbers, and does anyone know how to do it?
We round numbers to make them easier to work with, like when we have to add or subtract quickly.
So, we round to the nearest ten!
Exactly! For example, if our bill is ₹577.80, to the nearest ten, we'd round it to ₹580. Let's practice that together with different numbers!
Calculating 10%
🔒 Unlock Audio Lesson
Sign up and enroll to listen to this audio lesson
Now that we've rounded our bill to ₹580, let’s calculate 10% of this amount. Who can remind me how to find 10%?
To find 10%, we divide the number by ten.
So, that would be ₹580 ÷ 10, which is ₹58!
Perfect! So, we’ve found 10% of our estimated bill. Next, let's see how we can use this value.
Finding Half of 10%
🔒 Unlock Audio Lesson
Sign up and enroll to listen to this audio lesson
Now, to make estimating easier, we can find half of 10%. What is half of ₹58?
That would be ₹29!
Right again! By taking half of 10%, we simplify our calculations. Now let’s estimate the total discount.
Estimating Total Discount
🔒 Unlock Audio Lesson
Sign up and enroll to listen to this audio lesson
So far, we have ₹58 for 10% and ₹29 for half. What do we get when we add these two amounts?
Adding them gives us ₹87.
Yes! Therefore, we can estimate that the discount is about ₹87. Let's now find out how much we'd actually pay after the discount.
Calculating the Final Amount
🔒 Unlock Audio Lesson
Sign up and enroll to listen to this audio lesson
If we subtract our estimated discount of ₹87 from our rounded bill amount of ₹580, what do we get?
That would be ₹493!
Close, but remember the approximation, we could round that to ₹495. Can anyone summarize what we've learned today?
We learned to round the bill, find 10% and half of it, add to estimate the discount, and then calculate the final bill!
Introduction & Overview
Read summaries of the section's main ideas at different levels of detail.
Quick Overview
Standard
The section teaches how to estimate percentages by rounding numbers to the nearest ten, calculating 10% and 15% of an amount, and using these calculations to deduce the final payable amount after applying discounts. It emphasizes the importance of estimation in practical scenarios like shopping bills.
Detailed
Estimation in Percentages
Estimating percentages is a valuable skill for simplifying calculations in real-life situations, especially in shopping scenarios where discounts are commonly applied. This section discusses practical steps for estimating the amount to be paid after a discount.
Key Points Covered:
- Rounding Off: Begin by rounding the original bill amount to the nearest ten. For example, a bill of ₹577.80 can be rounded to ₹580.
- Calculating 10%: Once rounded, find 10% of the rounded figure. For ₹580, 10% is calculated as ₹58.
- Estimating Half: Next, half of this 10% value is computed. In this case, half of ₹58 is ₹29.
- Summing Estimates: The last step involves adding the amounts from the previous two steps to get a rough estimate of the percentage discount. Adding ₹58 (10%) and ₹29 (half) gives an estimate of ₹87.
- Final Amount Calculation: Subtract this estimated discount from the original rounded amount to arrive at the approximate final bill, which in this scenario would be ₹495 after applying the estimated discount.
This estimation method saves time and mental effort while shopping and helps in making quick decisions.
Youtube Videos
Audio Book
Dive deep into the subject with an immersive audiobook experience.
Rounding Off the Bill
Chapter 1 of 5
🔒 Unlock Audio Chapter
Sign up and enroll to access the full audio experience
Chapter Content
Your bill in a shop is ₹577.80 and the shopkeeper gives a discount of 15%. How would you estimate the amount to be paid?
(i) Round off the bill to the nearest tens of ₹577.80, i.e., to ₹580.
Detailed Explanation
To estimate the bill, the first step is to simplify the number by rounding it. Rounding off means changing a number to a simpler value that is approximately close to the original value. In this case, ₹577.80 rounds to ₹580 because we are looking at the nearest ten. When the number after the tens place (7 in this case) is 5 or more, we round up, and if it's less than 5, we round down.
Examples & Analogies
Think of rounding off like estimating the time it takes to bake a cake. If the recipe says it takes 37 minutes, you might tell your friends it takes about 40 minutes instead. It's an easy way to communicate and gives a good idea of how long it will take.
Finding 10% of the Rounded Bill
Chapter 2 of 5
🔒 Unlock Audio Chapter
Sign up and enroll to access the full audio experience
Chapter Content
(ii) Find 10% of this, i.e., ₹580 × 10% = ₹58.
Detailed Explanation
Now that we have rounded the bill to ₹580, we calculate 10% of this amount to estimate the discount. To find 10% of a number, you can simply divide that number by 10. In this case, ₹580 divided by 10 equals ₹58. This value gives us a rough idea of how much discount we will receive.
Examples & Analogies
Imagine you want to give a 10% tip at a restaurant. If your meal cost ₹580, calculating 10% is like slicing a piece of cake—you get a small portion, which in this case is ₹58. It makes deciding how much to tip easier.
Calculating Half of 10% for the Discount
Chapter 3 of 5
🔒 Unlock Audio Chapter
Sign up and enroll to access the full audio experience
Chapter Content
(iii) Take half of this, i.e., ₹58 ÷ 2 = ₹29.
Detailed Explanation
Next, we take half of the 10% amount calculated. This is because to find a 15% discount, you can think of it as 10% plus half of 10%. Hence, taking half of ₹58 gives us ₹29. This step helps us to get a clearer understanding of what a 15% discount approximately looks like.
Examples & Analogies
If you have 58 marbles and you want to share them evenly with your friend, you would be giving away half, which is 29 marbles. This sharing concept helps visualize how we are just splitting the 10% discount for 15%.
Adding to Find Total Estimated Discount
Chapter 4 of 5
🔒 Unlock Audio Chapter
Sign up and enroll to access the full audio experience
Chapter Content
(iv) Add the amounts in (ii) and (iii) to get ₹87.
Detailed Explanation
We now need to combine the amounts we've calculated: the 10% discount of ₹58 and half of that amount, ₹29. Adding these values together gives us ₹87. This value represents an estimated discount on the original bill due to the shopkeeper's provided percentage discount.
Examples & Analogies
Consider planning a party and needing supplies. If you estimate that balloons cost ₹58 and streamers cost ₹29, calculating the total you need to spend helps you better prepare your budget, just like estimating your discount total.
Estimating the Final Amount After Discount
Chapter 5 of 5
🔒 Unlock Audio Chapter
Sign up and enroll to access the full audio experience
Chapter Content
You could therefore reduce your bill amount by ₹87 or by about ₹85, which will be ₹495 approximately.
Detailed Explanation
To determine the final estimated amount to pay, we subtract the estimated discount of ₹87 from the rounded bill amount of ₹580. This means you would expect to pay approximately ₹495 after applying the discount, even though the exact amount may differ slightly.
Examples & Analogies
Imagine you're shopping for new shoes priced at ₹580 but find out there's a promise of savings. You can estimate how much you’ll actually part with—like planning for a trip where you've saved some money for expenses, which brings your final costs down.
Key Concepts
-
Rounding: Adjusting numbers for simplicity.
-
10% calculation: A foundational step in estimating.
-
Half of 10%: Simplifies estimation and aids calculations.
-
Final price calculation: Subtracting estimates from original amounts.
Examples & Applications
If a bill is ₹462.45, rounding is ₹460. 10% is ₹46, half is ₹23. Total estimated discount is about ₹69, making the final bill approximately ₹391.
Memory Aids
Interactive tools to help you remember key concepts
Rhymes
Round up, round down, to the nearest ten, estimating discounts again and again!
Stories
Once there was a shopper who rounded off their bill before knowing how much they saved. They felt like a magician, making money vanish with discounts!
Memory Tools
RSHF - Round, Subtract Half, Find total, calculate final amount.
Acronyms
RAD - Round, Apply discount, Determine final price.
Flash Cards
Glossary
- Estimate
An approximation of a value, often to make calculations simpler.
- Percentage
A fraction of 100, used to express how much of something exists relative to a whole.
- Rounding
Adjusting a number to the nearest specified value to simplify calculations.
Reference links
Supplementary resources to enhance your learning experience.