krit.club logo

A Trip to Bhopal - Estimation of Numbers

Grade 4CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

Rounding to the Nearest 10: Look at the digit in the ones place. If it is 5,6,7,8,5, 6, 7, 8, or 99, round up by adding 11 to the tens digit. If it is 0,1,2,3,0, 1, 2, 3, or 44, keep the tens digit the same. Visually, think of a number line: the number 2828 is closer to 3030 than 2020, so it rounds to 3030.

•

Rounding to the Nearest 100: Examine the tens digit. If the tens digit is 55 or more, round up to the next hundred; otherwise, round down. Imagine a 'Rounding Hill' where 5050 is the peak; any number like 149149 rolls back to 100100, but 150150 and above roll forward to 200200.

•

Estimation of Sums: To quickly guess a total, round each number to its nearest ten or hundred before adding. For example, if there are 3232 students in Class A and 3939 in Class B, the estimated total is 30+40=7030 + 40 = 70. This is helpful for planning bus seats for a trip.

•

Estimation of Differences: Round the numbers first, then subtract to find the approximate difference. If a bus tank holds 100100 litres and currently has 2222 litres, you can estimate that you need roughly 100−20=80100 - 20 = 80 litres more.

•

Calculating Total Capacity: To find the total number of people who can travel, multiply the number of buses by the seats per bus. Visually, imagine 55 buses as 55 large rectangles, each containing 5050 small squares (seats), representing 5×50=2505 \times 50 = 250 total seats.

•

Time Estimation: Calculate arrival times by adding the duration of the journey to the starting time. If the trip starts at 9:009:00 AM and takes 22 hours and 3030 minutes, the estimated arrival is 11:3011:30 AM. On a clock face, this involves moving the hour hand two steps and the minute hand halfway around.

•

The Unitary Method in Estimation: Find the value of one unit to estimate the value of many. If one lunch box costs Rs. 4545, you can round it to Rs. 5050 to estimate that 1010 boxes will cost about 10×50=50010 \times 50 = 500. This is like seeing the price for one item on a shelf and mentally multiplying it for a whole bag of items.

📐Formulae

Total Seats=Number of Buses×Seats per Bus\text{Total Seats} = \text{Number of Buses} \times \text{Seats per Bus}

Estimated Sum≈Rounded Number 1+Rounded Number 2\text{Estimated Sum} \approx \text{Rounded Number 1} + \text{Rounded Number 2}

Estimated Difference≈Rounded Number 1−Rounded Number 2\text{Estimated Difference} \approx \text{Rounded Number 1} - \text{Rounded Number 2}

Total Cost=Quantity×Price per unit\text{Total Cost} = \text{Quantity} \times \text{Price per unit}

Number of Buses Needed=Total StudentsSeats per Bus\text{Number of Buses Needed} = \frac{\text{Total Students}}{\text{Seats per Bus}}

💡Examples

Problem 1:

A group of 212212 children are going to Bhopal. Each bus has 5050 seats. Estimate how many buses are needed and how many children will be left without a seat if they get 44 buses.

Solution:

  1. Total children = 212212 \ 2. Number of buses = 44 \ 3. Seats per bus = 5050 \ 4. Total seats available = 4×50=2004 \times 50 = 200 seats \ 5. Children without seats = 212−200=12212 - 200 = 12 children.

Explanation:

We first calculate the total capacity of the buses using multiplication. Then, we subtract that capacity from the total number of students to find the remainder who do not have a seat.

Problem 2:

The bus stops to refill diesel at a pump. Each bus takes about 1515 minutes to refill. If there are 22 buses and they arrive at the pump at 11:0011:00 AM, at what time will they leave?

Solution:

  1. Refill time for 11 bus = 1515 minutes \ 2. Refill time for 22 buses = 15×2=3015 \times 2 = 30 minutes \ 3. Arrival time = 11:0011:00 AM \ 4. Departure time = 11:00 AM+30 minutes=11:30 AM11:00 \text{ AM} + 30 \text{ minutes} = 11:30 \text{ AM}.

Explanation:

We calculate the total time spent at the pump by multiplying the time per bus by the count of buses. Adding this duration to the arrival time gives the departure time.