What are the rules for the comparison of four-digit numbers?
We have already learnt that a two-digit number is always greater than a single digit number. But, in case of comparison of four-digit numbers, we must consider the following facts:
(i) The number having more digits is greater i.e., a four-digit number is always greater than a three-digit number, two-digit number or one-digit number separately. As:
1000 > 999 , 1000 > 798 , 1000 > 191 ,
3275 > 375 ,
5823 > 823 , 4378 > 937 , etc.
(a) The number having the greater extreme left digit, is the greater number.
5738 > 3561 , 9721 > 8925 , 2193 > 1293 as 5 > 3, 9 > 8, etc.
(b) If the digits on the extreme left are equal, then the rules to compare three-digit numbers are followed, as:
(i) 5738 > 5698 , 9794 > 9695 , 1548 > 1499
(ii) 5738 > 5729 , 9794 > 9784 , 1548 > 1529
(iii) 1968 > 1965 , 9798 > 9796 , 1548 > 1532
In general we can form the following rules to compare two or more numbers:
(a) If two numbers have equal number of digits, the number having greater valued digit on the extreme left is greater.
(b) If the digits on extreme left of the numbers are equal then the digits to the right of the extreme left digits are compared and so on.
Comparing and Arranging Numbers:
● Numbers are compared from the left to right.
● If the digits are equal at the place than compare on the right digit at the next place.
How to arrange 4-digit numbers in ascending and descending order:
(i) Arranging the numbers 2137, 1815, 3279, 4716, 3373 in ascending order:
The numbers are arranged in ascending order 1815, 2137, 3279, 3373, 4716.
(ii) Arranging the numbers 5204, 3418, 7432, 5855, 2195 in descending order:
The numbers are arranged in descending order 7432, 5855, 5204, 3418, 2195.
(iii) Arranging the numbers 6001, 3145, 1111, 2157, 4679 in ascending order:
The numbers are arranged in ascending order 1111, 2157, 3145, 4679, 6001.
(iv) Arranging the numbers 3004, 3098, 3382, 3531, 3461 in descending order:
The numbers are arranged in descending order 3531, 3461, 3382, 3098, 3004.
Thus, any five-digit number is always greater than a four-digit number and so on...
Questions and answers on Comparing and Arranging Numbers:
I. Circle the smallest and Tick ( ) the largest in the given sets:
(i) 7920 8209 6305 5706 4321
(ii) 5248 2990 3841 4801 6549
(iii) 3832 5042 8700 9354 4672
(iv) 1832 2832 3845 2700 6840
(v) 7548 4241 3975 9410 6942
(vi) 4421 3785 9441 8961 7265
(vii) 3934 7620 8344 5287 9762
(viii) 9843 2489 6765 4329 3349
(ix) 2728 5964 4378 8957 7862
(x) 9397 3583 7621 2582 8955
Answer:
I. (i) Smallest - 4321; Largest - 8209
(ii) Smallest - 2990; Largest - 6549
(iii) Smallest - 3832; Largest - 9354
(iv) Smallest - 1832; Largest - 6840
(v) Smallest - 3975; Largest - 9410
(vi) Smallest - 3785; Largest - 9441
(vii) Smallest - 3934; Largest - 9762
(viii) Smallest - 2489; Largest - 9843
(ix) Smallest - 2728; Largest - 8957
(x) Smallest - 2582; Largest - 9397
II. Write >, < or = :
(i) 2536 ……….. 2160
(ii) 7328 ……….. 7934
(iii) 4653 ……….. 4653
(iv) 6000 ……….. 5999
(v) 3924 ……….. 3910
(vi) 9320 ……….. 9245
(vii) 8888 ……….. 8888
(viii) 7542 ……….. 7642
(ix) 6789 ……….. 6542
(x) 8089 ……….. 8320
(xi) 4638 ……….. 3250
(xii) 5644 ……….. 5646
(xiii) 4878 ……….. 4878
(xiv) 5555 ……….. 5554
(xv) 7824 ……….. 3219
Answer:
II. (i) >
(ii) <
(iii) =
(iv) >
(v) >
(vi) >
(vii) =
(viii) <
(ix) >
(x) <
(xi) >
(xii) <
(xiii) =
(xiv) >
(xv) >
III. Write the smallest number in each set:
(i) 4291 3161 5026 1203 1689
(ii) 3167 7052 3200 4623 4320
(iii) 4290 3261 9875 9891 3483
(iv) 3261 4883 4290 5875 6891
(v) 5290 3126 4891 1834 7999
Answer:
III. (i) 1203
(ii) 3200
(iii) 3261
(iv) 3261
(v) 1834
IV. Write the biggest number in each set:
(i) 3120 4619 8207 5213 4679
(ii) 6257 3217 3271 9871 3527
(iii) 1326 2578 4729 5017 6025
(iv) 8054 3200 4700 9602 8309
(v) 1001 2007 3005 3850 5810
Answer:
IV. (i) 8207
(ii) 9871
(iii) 6025
(iv) 9602
(v) 5810
V. Write the descending order (from the biggest to the smallest):
(i) 1100 8800 2146 4239 1348 3746
(ii) 2644 3179 5341 8072 1528 7947
(iii) 2937 8456 5119 6098 4050 3433
(iv) 8532 4729 7811 3502 5238 3333
(v) 6584 6548 6458 6845 6485 6854
Answer:
V. (i) 8800, 4239, 3746, 2146, 1348, 1100
(ii) 8072, 7947, 5341, 3179, 2644, 1528
(iii) 8456, 6098, 5119, 4050, 3433, 2937
(iv) 8532, 7811, 5238, 4729, 3502, 3333
(v) 6854, 6845, 6584, 6548, 6485, 6458
VI. Write the ascending order (from the smallest to the biggest):
(i) 3294 3924 3492 3942 3429 3249
(ii) 2842 1395 8075 6207 5384 3946
(iii) 1378 1597 2845 7309 9098 7301
(iv) 3764 2245 2834 8843 4878 2349
(v) 4123 1532 4332 5023 3842 5382
Answer:
VI. (i) 3249, 3294, 3429, 3492, 3924, 3942
(ii) 1395, 2842, 3946, 5384, 6207, 8075
(iii) 1378, 1597, 2845 7301, 7309, 9098
(iv) 2245, 2349, 2834, 3764, 4878, 8843
(v) 1532, 3842, 4123, 4332, 5023, 5382
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