RBSE Solutions Class 6 Maths Chapter 1 Know the Numbers Exercise 1.3

Question 1. Replace each number to the nearest hundred of the following and calculate the answer again in the nearest hundred.
(i) \( 247 + 691 \)
(ii) \( 4316 + 1567 \)
(iii) \( 7122 - 3565 \)
(iv) \( 4543 - 2036 \)
Answer:
(i) For \( 247 + 691 \):
The tens digit in 247 is 4. Since 4 is less than 5, 247 rounds down to the nearest hundred, which is 200.
The tens digit in 691 is 9. Since 9 is greater than 5, 691 rounds up to the nearest hundred, which is 700.
Adding the rounded numbers, \( 200 + 700 = 900 \). Rounding helps us estimate quickly without needing exact calculations.
(ii) For \( 4316 + 1567 \):
The tens digit in 4316 is 1. As 1 is less than 5, 4316 rounds down to the nearest hundred, which is 4300.
The tens digit in 1567 is 6. Since 6 is greater than 5, 1567 rounds up to the nearest hundred, which is 1600.
Adding the rounded numbers gives \( 4300 + 1600 = 5900 \). This rounding process simplifies large numbers, making mental math easier.
(iii) For \( 7122 - 3565 \):
The tens digit in 7122 is 2. Since 2 is less than 5, 7122 rounds down to the nearest hundred, which is 7100.
The tens digit in 3565 is 6. As 6 is greater than 5, 3565 rounds up to the nearest hundred, which is 3600.
Subtracting the rounded numbers gives \( 7100 - 3600 = 3500 \). Knowing how to round helps verify if an exact calculation result is reasonable.
(iv) For \( 4543 - 2036 \):
The tens digit in 4543 is 4. Since 4 is less than 5, 4543 rounds down to the nearest hundred, which is 4500.
The tens digit in 2036 is 3. Since 3 is less than 5, 2036 also rounds down to the nearest hundred, which is 2000.
Subtracting the rounded numbers gives \( 4500 - 2000 = 2500 \). Rounding is a useful skill for quick mental calculations and for checking the approximate correctness of more precise answers.
In simple words: First, round each number to the nearest hundred. If the tens digit is 5 or more, round up; otherwise, round down. Then, perform the addition or subtraction with the rounded numbers.

🎯 Exam Tip: When rounding to the nearest hundred, always look at the tens digit. If it's 5 or greater, round the hundreds digit up. If it's 4 or less, keep the hundreds digit the same and change the tens and ones digits to zero.

Question 2. Multiply the nearest tens numbers of the following :
(i) \( 34 \times 57 \)
(ii) \( 294 \times 72 \)
(iii) \( 869 \times 675 \)
Answer:
(i) For \( 34 \times 57 \):
To round 34 to the nearest ten, we look at the ones digit. Since 4 is less than 5, 34 rounds down to 30.
For 57, the ones digit is 7. Since 7 is 5 or more, 57 rounds up to 60.
Multiplying these rounded numbers gives \( 30 \times 60 = 1800 \). Rounding to the nearest ten is useful for estimating products quickly.
(ii) For \( 294 \times 72 \):
To round 294 to the nearest ten, the ones digit is 4. Since 4 is less than 5, 294 rounds down to 290.
For 72, the ones digit is 2. Since 2 is less than 5, 72 rounds down to 70.
Multiplying these rounded numbers gives \( 290 \times 70 = 20300 \). Estimating helps catch large errors in exact calculations.
(iii) For \( 869 \times 675 \):
To round 869 to the nearest ten, the ones digit is 9. Since 9 is 5 or more, 869 rounds up to 870.
For 675, the ones digit is 5. Since 5 is 5 or more, 675 rounds up to 680.
Multiplying these rounded numbers gives \( 870 \times 680 = 591600 \). Rounding can be very practical for budgeting or quick financial checks.
In simple words: Round each number to its nearest ten by looking at the ones digit. If it's 5 or more, round up; if less than 5, round down. Then, multiply the rounded numbers together.

🎯 Exam Tip: When rounding to the nearest ten, focus on the ones digit. If it's 5 or more, increase the tens digit by one and make the ones digit zero. If it's less than 5, keep the tens digit as it is and make the ones digit zero.

Question 3. In the school library, there are 2541 books of stories, 1017 subject books and other books are 857. Find out the approximate number of books in the school. (Rounding the number to 100).
Answer:
The number of story books is 2541. When rounded to the nearest hundred, 2541 becomes 2500 (since the tens digit 4 is less than 5).
The number of subject books is 1017. When rounded to the nearest hundred, 1017 becomes 1000 (since the tens digit 1 is less than 5).
The number of other books is 857. Rounded to the nearest hundred, 857 becomes 900 (since the tens digit 5 is 5 or more).
To find the approximate total number of books, we add the rounded figures: \( 2500 + 1000 + 900 = 4400 \). Rounding helps simplify calculations when an exact total isn't strictly necessary, providing a good estimate.
In simple words: Round the number of story books (2541) to 2500. Round the number of subject books (1017) to 1000. Round the number of other books (857) to 900. Add these rounded numbers: 2500 + 1000 + 900 = 4400. So, there are approximately 4400 books in total.

🎯 Exam Tip: Always remember to round each number *before* performing the main calculation (addition or subtraction) when asked for an approximate answer, as rounding after calculating would give a different result.

Question 5. A car runs 15 kilometer with 1 litre petrol. How much petrol does it need to go 100 kms? (Find out the value rounding the number to 10).
Answer:
For every 15 kilometers, the car uses 1 litre of petrol.
To find out how much petrol is needed for 1 kilometer, we divide 1 litre by 15 kilometers: \( \frac { 1 }{ 15 } \) litre.
So, for 100 kilometers, the petrol needed will be \( \frac { 1 \times 100 }{ 15 } = \frac { 100 }{ 15 } \) litres.
\( \frac { 100 }{ 15 } = 6.666... \) litres. Rounding this value to the nearest whole number (since the first decimal is 6, which is 5 or more) gives approximately 7 litres. Understanding how to calculate fuel efficiency helps manage travel costs and plan trips effectively.
In simple words: The car uses 1 litre of petrol for 15 km. To go 100 km, it needs \( \frac{100}{15} \) litres. This is about 6.67 litres. Rounding to the nearest whole number, the car needs approximately 7 litres of petrol.

🎯 Exam Tip: When solving problems involving distance and fuel consumption, always first calculate the consumption for a single unit (e.g., 1 km or 1 litre) before scaling it up for the total required amount.