GSEB Class 6 Maths Solutions Chapter 1 Knowing Our Numbers Exercise 1.3

Question 1. Estinwie each of the following using general rule:
(a) 730 + 998
(b) 796-314
(c) 12,904 + 2,888
(d) 28,292 – 21.496
Answer:
(a) For \( 730 + 998 \):
\( 730 \rightarrow 700 \) (Rounded off to hundreds)
\( 998 \rightarrow 1000 \) (Rounded off to hundreds)
Estimated sum \( = 700 + 1000 = 1700 \)
(b) For \( 796 - 314 \):
\( 796 \rightarrow 800 \) (Rounded off to hundreds)
\( 314 \rightarrow 300 \) (Rounded off to hundreds)
Estimated difference \( = 800 - 300 = 500 \)
(c) For \( 12,904 + 2888 \):
\( 12,904 \rightarrow 13,000 \) (Rounded off to hundreds)
\( 2,888 \rightarrow 3,000 \) (Rounded off to hundreds)
Estimated sum \( = 13,000 + 3,000 = 16,000 \)
(d) For \( 28,292 - 21,496 \):
\( 28,292 \rightarrow 28,000 \) (Rounded off to hundreds)
\( 21,496 \rightarrow 21,000 \) (Rounded off to hundreds)
Estimated difference \( = 28000 - 21000 = 7000 \)
In simple words: To estimate, first round each number to the nearest hundred or thousand. Then, add or subtract these rounded numbers to get the estimated sum or difference.

Exam Tip: When estimating, always clarify the place value you are rounding to (e.g., hundreds, thousands) as this affects the final outcome. State the rounding rule explicitly.

Question 2. Give a rough estimate (By rounding off to nearest hundreds) and also a closer estimate (by rounding off to nearest tens):
(a) 439 + 334 + 4,317
(b) 1,08,734 – 47,599
(c) 8,325-491
(d) 4,89,348 – 48,365
Answer:
(a) For \( 439 + 334 + 4,317 \):
Rough estimate (rounding to hundreds):
\( 439 \rightarrow 400 \)
\( 334 \rightarrow 300 \)
\( 4,317 \rightarrow 4,300 \)
Rough estimate \( = 400 + 300 + 4300 = 5,000 \)
Closer estimate (rounding to tens):
\( 439 \rightarrow 440 \)
\( 334 \rightarrow 330 \)
\( 4,317 \rightarrow 4,320 \)
Closer estimate \( = 440 + 330 + 4,320 = 5,090 \)
(b) For \( 1,08,734 - 47,599 \):
Rough estimate (rounding to hundreds):
\( 1,08,734 \rightarrow 1,08,700 \)
\( 47,599 \rightarrow 47,600 \)
Rough estimate \( = 1,08,700 - 47,600 = 61,100 \)
Closer estimate (rounding to tens):
\( 1,08,734 \rightarrow 1,08,730 \)
\( 47,599 \rightarrow 47,600 \)
Closer estimate \( = 1,08,730 - 47,600 = 61,130 \)
(c) For \( 8,325 - 491 \):
Rough estimate (rounding to hundreds):
\( 8,325 \rightarrow 8,300 \)
\( 491 \rightarrow 500 \)
Rough estimate \( = 8,300 - 500 = 7,800 \)
Closer estimate (rounding to tens):
\( 8,325 \rightarrow 8,330 \)
\( 491 \rightarrow 490 \)
Closer estimate \( = 8,330 - 490 = 7,840 \)
(d) For \( 4,89,348 - 48,365 \):
Rough estimate (rounding to hundreds):
\( 4,89,348 \rightarrow 4,89,300 \)
\( 48,365 \rightarrow 48,400 \)
Rough estimate \( = 4,89,300 - 48,400 = 4,40,900 \)
Closer estimate (rounding to tens):
\( 4,89,348 \rightarrow 4,89,350 \)
\( 48,365 \rightarrow 48,370 \)
Closer estimate \( = 4,89,350 - 48,370 = 4,40,980 \)
In simple words: First, round numbers to the nearest hundred for a quick "rough estimate." Then, round them to the nearest ten for a more precise "closer estimate." Finally, perform the addition or subtraction with these rounded numbers.

Exam Tip: Always clearly label whether you're performing a rough or closer estimate and state the place value to which you are rounding. This helps show your understanding of estimation techniques.

Question 3. Estimate the following products using general rule:
(a) 578 x 161
(b) 5,281 x 3,491
(c) 1,291 x 592
(d) 9,250 x 29
Answer:
(a) For \( 578 \times 161 \):
\( 578 \rightarrow 600 \) (Rounding off to hundreds)
\( 161 \rightarrow 200 \) (Rounding off to hundreds)
Estimated product \( = 600 \times 200 = 1,20,000 \)
(b) For \( 5,281 \times 3,491 \):
\( 5,281 \rightarrow 5,000 \) (Rounding off to thousands)
\( 3,491 \rightarrow 3,500 \) (Rounding off to hundreds)
Estimated product \( = 5,000 \times 3,500 = 1,75,00,000 \)
(c) For \( 1,291 \times 592 \):
\( 1,291 \rightarrow 1,300 \) (Rounding off to hundreds)
\( 592 \rightarrow 600 \) (Rounding off to hundreds)
Estimated product \( = 1,300 \times 600 = 7,80,000 \)
(d) For \( 9,250 \times 29 \):
\( 9,250 \rightarrow 9,300 \) (Rounding off to hundreds)
\( 29 \rightarrow 30 \) (Rounding off to tens)
Estimated product \( = 9300 \times 30 = 279000 \)
In simple words: To estimate products, round each number to a suitable place value (like the nearest hundred or thousand, or ten). Then, multiply the rounded numbers together to get an approximate answer.

Exam Tip: When estimating products, it's crucial to select appropriate rounding levels for each number to maintain reasonable accuracy. Rounding factors to the nearest ten, hundred, or thousand makes calculations simpler.