Samacheer Kalvi Class 6 Maths Solutions Term 1 Chapter 1 Numbers Exercise 1.4

Question 1. Fill in the blanks.
(i) The nearest 100 of 843 is _____
(ii) The nearest 1000 of 756 is _____
(iii) The nearest 10,000 of 85654 is _____
Answer:
(i) 800.
To round 843 to the nearest 100, look at the tens digit. The tens digit is 4, which is less than 5. So, we round down to 800.
(ii) 1000.
To round 756 to the nearest 1000, look at the hundreds digit. The hundreds digit is 7, which is 5 or more. So, we round up to 1000.
(iii) 90,000.
To round 85654 to the nearest 10,000, look at the thousands digit. The thousands digit is 5, which is 5 or more. So, we round up to 90,000.
In simple words: To round numbers, check the digit just to the right of the place you are rounding to. If it's 5 or more, round up; if it's less than 5, round down.

🎯 Exam Tip: Always identify the 'rounding place' first, then look at the digit immediately to its right to decide whether to round up or down. Pay attention to the specific place value requested (tens, hundreds, thousands, etc.).

Question 2. Say True or False
(i) 8567 is rounded off as 8600 to the nearest 10.
(ii) 139 is rounded off as 100 to the nearest 100.
(iii) 1,70,51,972 is rounded off as 1,70,00,000 to the nearest lakh.
Answer:
(i) False
To round 8567 to the nearest 10, we look at the ones digit. The ones digit is 7, which is 5 or more. So, we round up the tens digit (6) to 7. This gives 8570, not 8600. So the statement is false.
(ii) True
To round 139 to the nearest 100, we look at the tens digit. The tens digit is 3, which is less than 5. So, we round down to 100. This statement is true.
(iii) False
To round 1,70,51,972 to the nearest lakh (1,00,000), we look at the ten thousands digit. The ten thousands digit is 5, which is 5 or more. So, we round up the lakhs digit (0) to 1. This would give 1,71,00,000. Therefore, the given rounding of 1,70,00,000 is false.
In simple words: Look at the digit next to the place you are rounding to. If it's 5 or more, round up. If it's less than 5, keep the digit the same and turn the rest to zero.

🎯 Exam Tip: Be careful with large numbers and Indian numbering system terms like 'lakh' (which means 100,000). Always check the digit in the place value immediately to the right of the rounding place.

Question 3. Round off the following to the given nearest place.
(i) 4,065; hundred
(ii) 44,555; thousand
(iii) 86,943; ten thousand
(iv) 50,81,739; lakh
(v) 33,75,98,482; ten crore
Answer:
(i) 4100
(ii) 45,000
(iii) 90,000
(iv) 51,00,000
(v) 30,00,00,000
In simple words: For each number, find the place value mentioned (like hundred, thousand, lakh) and then look at the digit just after it to decide if you round up or down. Change all digits after the rounding place to zero.

🎯 Exam Tip: Clearly identify the digit that determines rounding. For example, when rounding to the nearest hundred, the tens digit is the key. When rounding to the nearest lakh, the ten thousands digit is the key.

Question 4. Estimate the sum of 157826 and 32469 rounded off to the nearest ten thousand.
Answer: First, let's find the actual sum:
\( 157826 + 32469 = 190295 \)
Now, we round this sum to the nearest ten thousand. The number is 190295.
The ten thousands digit is 9. We look at the thousands digit, which is 0. Since 0 is less than 5, we round down. So the number becomes 1,90,000.
Therefore, the estimated sum rounded to the nearest ten thousand is 1,90,000.
In simple words: First, add the two numbers together. Then, take the total and round it to the nearest ten thousand. This means checking the thousands digit to see if you round up or down.

🎯 Exam Tip: When asked to estimate a sum or difference by rounding, perform the original operation first, and then round the final result unless specified otherwise. Always show the intermediate sum before rounding.

Question 5. Estimate by rounding off each number to the nearest hundred.
(i) 8074 + 4178
(ii) 1768977 + 130589
Answer:
(i) For 8074 + 4178:
Actual sum \( = 8074 + 4178 = 12252 \)
Rounding 12252 to the nearest hundred: The tens digit is 5, so we round up. The estimated sum is 12,300.
(ii) For 1768977 + 130589:
Actual sum \( = 1768977 + 130589 = 1899566 \)
Rounding 1899566 to the nearest hundred: The tens digit is 6, so we round up. The estimated sum is 18,99,600.
In simple words: Add the numbers normally. Then, take the total and round it to the nearest hundred. Look at the tens digit to decide if you round up or down.

🎯 Exam Tip: Pay close attention to the instruction. If it asks to round *each number* first and *then* estimate, follow that. If it just says "estimate by rounding off," rounding the final sum is often acceptable unless context implies otherwise.

Question 6. The population of a city was 43,43,645 in the year 2001 and 46,81,087 in the year 2011. Estimate the increase in population by rounding off to the nearest thousands.
Answer: Population in 2001 \( = 43,43,645 \)
Population in 2011 \( = 46,81,087 \)
First, we calculate the actual increase in population:
Increase in population \( = 46,81,087 - 43,43,645 = 3,37,442 \)
Now, we estimate this increase by rounding to the nearest thousand. The number is 3,37,442.
The thousands digit is 7. We look at the hundreds digit, which is 4. Since 4 is less than 5, we round down. So the number becomes 3,37,000.
Therefore, the estimated increase in population rounded to the nearest thousands is 3,37,000.
In simple words: First, find out how much the population grew by subtracting the old number from the new one. Then, round that answer to the nearest thousand by checking the hundreds digit.

🎯 Exam Tip: For problems involving estimations, clearly state the actual calculation and then show the rounding step. Make sure to identify the correct place value for rounding as specified in the question.

Objective Type Questions

Question 7. The number which on rounding off to the nearest thousand gives 11000 is
(a) 10345
(b) 10855
(c) 11799
(d) 10056
Answer: (b) 10855
In simple words: To get 11000 when rounding to the nearest thousand, the original number must be between 10500 and 11499. Out of the given choices, 10855 is the only number that fits this rule.

🎯 Exam Tip: To find a number that rounds to a specific value, identify the range of numbers that would round to that value. For rounding to the nearest thousand, the range is usually from 500 below to 499 above the rounded value.

Question 8. The estimation to the nearest hundredth of 76812 is
(a) 77000
(b) 76000
(c) 76800
(d) 76900
Answer: (c) 76800
In simple words: To round 76812 to the nearest hundred, we look at the tens digit. The tens digit is 1, which is less than 5. So, we keep the hundreds digit as 8 and change the rest to zeroes, making it 76800.

🎯 Exam Tip: When rounding to the nearest hundred, the digit in the tens place is the deciding factor. If it's 0-4, round down; if it's 5-9, round up.

Question 9. The number 9785764 is rounded off to the nearest lakh as
(a) 9800000
(b) 9786000
(c) 9795600
(d) 9795000
Answer: (a) 9800000
In simple words: To round 9785764 to the nearest lakh (100,000), we look at the ten thousands digit. This digit is 8, which is 5 or more, so we round up the lakhs digit (7) to 8. This makes the number 98,00,000.

🎯 Exam Tip: Understand the Indian place value system (lakhs, crores). A lakh is 100,000. So, rounding to the nearest lakh means considering the digit in the ten thousands place.

Question 10. The estimated difference of 167826 and 2765 rounded off to the nearest thousand is
(a) 180000
(b) 165000
(c) 140000
(d) 155000
Answer: (b) 165000
In simple words: First, find the difference between 167826 and 2765. Then, take that answer and round it to the nearest thousand. You do this by looking at the hundreds digit.

🎯 Exam Tip: Similar to sums, for estimated differences, calculate the actual difference first and then round the final result to the specified place value, in this case, the nearest thousand.