Chapter - 1 -EXERCISE 1.3 - Knowing our Numbers Numbers (NCERT Class 6th Maths Solution)

1. Estimate each of the following using general rule:
(a) 730 + 998                                       (b) 796 – 314
(c) 12,904 +2,888                                (d) 28,292 – 21,496
Make ten more such examples of addition, subtraction and estimation of their outcome.

Solution/Explanation:

(a) 730 + 998 Round off to hundreds 730 is rounds off to 700 998 is rounds off to 1000 Hence, 730 + 998 = 700 + 1000 = 1700

(b) 796 – 314 Round off to hundreds 796 is rounds off to 800 314 is rounds off to 300 Hence, 796 – 314 = 800 – 300 = 500

(c) 12904 + 2888 Round off to thousands 12904 is rounds off to 13000 2888 is rounds off to 3000 Hence, 12904 + 2888 = 13000 + 3000 = 16000

(d) 28292 - 21496 Round off to thousands 28292 is round off to 28000 21496 is round off to 21000 Hence, 28292 – 21496 = 28000 – 21000 = 7000

Ten more such examples are
(i) 330 + 280 = 300 + 300 = 600
(ii) 3937 + 5990 = 4000 + 6000 = 10000
(iii) 6392 – 3772 = 6000 – 4000 = 2000
(iv) 5440 – 2972 = 5000 – 3000 = 2000
(v) 2175 + 1206 = 2000 + 1000 = 3000
(vi) 1110 – 1292 = 1000 – 1000 = 0
(vii) 910 + 575 = 900 + 600 = 1500
(viii) 6400 – 4900 = 6000 – 5000 = 1000
(ix) 3731 + 1300 = 4000 + 1000 = 5000
(x) 6485 – 4319 = 6000 – 4000 = 2000

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) 8325 – 491                                                  (d) 4,89,348 – 48,365
Make four more such examples.

Solution/Explanation:

(a) 439+334+4317${\displaystyle 439+334+4317}$
When rounding off to nearest hundreds,
400+300+4300=5000${\displaystyle 400+300+4300=5000}$
When rounding off to nearest tens,
440+330+4320=5090${\displaystyle 440+330+4320=5090}$

(b) 108734−47599${\displaystyle 108734-47599}$
When rounding off to nearest hundreds,
108700−47600=61400${\displaystyle 108700-47600=61400}$
When rounding off to nearest tens,
108730−47600=61430${\displaystyle 108730-47600=61430}$

(c) 8325−491${\displaystyle 8325-491}$
When rounding off to nearest hundreds,
8300−500=7800${\displaystyle 8300-500=7800}$
When rounding off to nearest tens,
8330−490=7840${\displaystyle 8330-490=7840}$

(d) 489348−48365${\displaystyle 489348-48365}$
When rounding off to nearest hundreds,
489300−48400=440900${\displaystyle 489300-48400=440900}$
When rounding off to nearest tens,
489350−48370=440980

3. Estimate the following products using general rule:
(a) 578 × 161                                             (b) 5281 × 3491
(c) 1291 × 592                                           (d) 9250 × 29
Make four more such examples.

Solution/Explanation:

(a) 578⋅161${\displaystyle 578\cdot 161}$
578→600,161=200${\displaystyle 578\to 600,161=200}$
600⋅200=120000${\displaystyle 600\cdot 200=120000}$
(b) 5281⋅3491${\displaystyle 5281\cdot 3491}$
5281→5000,3491→3000${\displaystyle 5281\to 5000,3491\to 3000}$
5000⋅3000=15000000${\displaystyle 5000\cdot 3000=15000000}$
(c) 1291⋅592${\displaystyle 1291\cdot 592}$
1291→1000${\displaystyle 1291\to 1000}$
592→600${\displaystyle 592\to 600}$
1000⋅600=600000${\displaystyle 1000\cdot 600=600000}$
(d) 9250⋅29${\displaystyle 9250\cdot 29}$
9250→9000,29→30${\displaystyle 9250\to 9000,29\to 30}$
9000⋅30=270000${\displaystyle 9000\cdot 30=270000}$
examples are
1) 341⋅128${\displaystyle 341\cdot 128}$
341→300,128→100${\displaystyle 341\to 300,128\to 100}$
300⋅100=30000${\displaystyle 300\cdot 100=30000}$
2) 568⋅831${\displaystyle 568\cdot 831}$
568→600,831→800${\displaystyle 568\to 600,831\to 800}$
600⋅800=480000${\displaystyle 600\cdot 800=480000}$
3) 1782⋅332${\displaystyle 1782\cdot 332}$
1782→2000,332→300${\displaystyle 1782\to 2000,332\to 300}$
2000⋅300=600000${\displaystyle 2000\cdot 300=600000}$
4) 8792⋅3777${\displaystyle 8792\cdot 3777}$
8792→9000,3777→4000${\displaystyle 8792\to 9000,3777\to 4000}$
9000⋅4000=36000000