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Compare and order these numbers using the given methods. Use signs (<, >, =) for comparison and arrange in ascending order.

Mathematics

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Answer

b
7666, 13654, 16236, 236591
16923, 19462, 37642, 48421
1534, 35243, 156191, 335461

Step-by-step solution

4 steps

Here are the solutions to the comparison and ordering problems:

Part a· 2 steps

Compare each pair of numbers using signs (<<, >>, or ==)

  1. Compare the number of digits.

    If they are different, the number with more digits is larger.

  2. If the number of digits is the same, compare digits from left to right until a difference is found.

    1. Compare 123654 and 335461. Both numbers have 6 digits. Comparing the first digit: 1<31 < 3. 123654<335461123654 < 335461
    2. Compare 76732 and 42654. Both numbers have 5 digits. Comparing the first digit: 7>47 > 4. 76732>4265476732 > 42654
    3. Compare 19452 and 19261. Both numbers have 5 digits. Comparing from left: 1=11=1, 9=99=9, then 4>24 > 2. 19452>1926119452 > 19261
    4. Compare 352431 and 352431. Both numbers are identical. 352431=352431352431 = 352431
    5. Compare 37642 and 334952. 37642 has 5 digits, 334952 has 6 digits. A 5-digit number is smaller than a 6-digit number. 37642<33495237642 < 334952

Part b7666, 13654, 16236, 236591

Arrange in ascending order

  1. Count the number of digits for each number.

    Numbers with fewer digits are smaller.

  2. For numbers with the same number of digits, compare them from left to right.

    1. Numbers: 13654,236591,16236,766613654, 236591, 16236, 7666

      • 7666 (4 digits)
      • 13654 (5 digits)
      • 16236 (5 digits)
      • 236591 (6 digits) Comparing the 5-digit numbers: 13654<1623613654 < 16236. Ascending order: 7666,13654,16236,236591\boxed{7666, 13654, 16236, 236591}
    2. Numbers: 16923,19462,48421,3764216923, 19462, 48421, 37642 All numbers have 5 digits.

      • Compare first digits: 1,1,4,31, 1, 4, 3.
      • Smallest are 16923 and 19462. Comparing these: 16923<1946216923 < 19462.
      • Next is 37642.
      • Largest is 48421. Ascending order: 16923,19462,37642,48421\boxed{16923, 19462, 37642, 48421}
    3. Numbers: 335461,35243,156191,1534335461, 35243, 156191, 1534

      • 1534 (4 digits)
      • 35243 (5 digits)
      • 156191 (6 digits)
      • 335461 (6 digits) Comparing the 6-digit numbers: 156191<335461156191 < 335461. Ascending order: 1534,35243,156191,335461\boxed{1534, 35243, 156191, 335461}
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