4
Comparing natural numbers
Textbook: Part 1, lesson 4, pp. 20–21
GoalCompare natural numbers on the number ray and by places; write a double inequality.
New words
inequality · tengsizlikdouble inequality · qo‘sh tengsizlikgreater · kattaless · kichik
Explanation
On the number ray, the number lying further left is smaller: 5 < 8 because A(5) is to the left of B(8). The number 8 is greater than 5 but less than 10; we write it as the double inequality 5 < 8 < 10. Of two numbers with different numbers of digits, the one with more digits is greater. If the numbers have the same number of digits, compare the digits place by place from the left. At the first place where they differ, the number with the smaller digit is the smaller number.
Worked examples
4 276 and 987: 4 276 has four digits, 987 has three. So 4 276 > 987.
507 318 and 507 291: 5=5, 0=0, 7=7, but 3 > 2. So 507 318 > 507 291.
Class activity
“Which is greater?”: two pupils write six-digit numbers on the board; the class compares digits from the left and puts « > » or « < ».
Practice
1
Compare: 90 405 and 9 405.
90 405 > 9 405
2
Compare: 7 654 321 and 7 654 312.
7 654 321 > 7 654 312
3
Write “47 is greater than 39 but less than 52” as a double inequality.
39 < 47 < 52
4
Why is 100 000 greater than 99 999?
100 000 has six digits and 99 999 has five; the one with more digits is greater.