Comparing numbers is important to know which number is greater and which number is smaller.
Solved examples for comparing numbers:
1. Compare the number 125 and 87 and find which number is the greater number.
Solution:
1 hundred 2 tens 5 ones = 125 = 12 tens and 5 ones
= 8 tens and 45 ones
8 tens 7 ones = 87 = 8 tens and 7 ones
125 = 8 tens + 45 ones
87 = 8 tens + 7 tens
It is clear 45 ones > 7 ones
or, 125 ones > 87 ones
or, 125 > 87
Therefore, the number which has more digits than the other is greater
2. Compare 238
and 148.
Solution:
2 hundred 3 tens 8 ones = 238 = 200 + 30 + 8
1 hundred 4 tens 8 ones = 148 = 100 + 40 + 8
238 = 200 + 30 + 8 = 238 ones
148 = 100 + 40 + 8 =148 ones
It is clear 238 ones > 148 ones.
Hence, 238 > 148 and 148 < 238
Both 238 and 148 have the same number of digits but the digit at hundreds place in 238 has higher place value (200) than the digit at hundreds place value in 148 i.e., (100) or 2 > 1.
Therefore, 238 > 148
3. Compare the following numbers:
(i) 256 and 234
Solution:
2 hundreds + 5 tens + 6 ones = 200 + 50 + 6 = 256 ones
2 hundreds +3 tens + 4 ones =200 + 30 + 4 = 234 ones
256 ones > 234 ones
or, 256 > 234
Both the number have equal number of hundreds, but 256 has more tens 234
Therefore, 256 > 234
(ii) 182 and 186
Solution:
1 hundred + 8 tens + 2 ones = 100 + 80 + 2 = 182 ones
1 hundred + 8 tens + 6 ones = 100 + 80 + 6 = 186 ones
or, 182 < 186
Both the numbers have equal number of hundreds and equal number of tens. But 182 has less ones than 186.
Therefore, 182 < 186
Notes for comparing numbers:
(i) The number having more hundred is greater
(ii) If the number has equal hundreds as the other number, but greater tens than the other, it is greater.
(iii) If one number has equal hundreds and equal tens but more ones than the other, it is greater.
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