Page 69 - Ganit Kaushal

3.5 COMPARING NUMBERS

Understanding how to compare numbers is crucial for making better judgements in our day-to-day lives.
For example: We compare the market prices of various air conditioners so that we can buy one according to
our budget. We may compare the GDP figures of different countries to determine which country has a larger
economy, or compare the populations of two cities to find out which is larger etc.
For comparing two numbers, we use the following rules:

(i) The more the number of digits, the greater is the number.
(ii) If two numbers have the same number of digits, the number with the bigger digit in the greatest
place is greater.
(iii) If two numbers have the same number of digits and the digit in the greatest place is also the same,
then we check the bigger digit in the next place to the right, and so on.
Comparing one-digit and two-digit numbers has already been done in earlier classes. Here, let’s give a few
examples of comparing numbers with three or more digits to explain the three rules given above.

(a) 732 < 965, 247 >169, 597 < 795, 908 > 809 [By rule (ii)]
(b) 439 > 421, 540 > 539, 994 > 989, 888 > 879 [By rule (iii)]

(c) 449 > 444, 997 > 992 [By rule (iii)]
(d) 7529 > 6983 because 7 > 6 [By rule (ii)]

(e) 45819 > 25918 because 4 > 2 [By rule (ii)]
(f) 90526 > 9998 (greater no. of digits) [By rule (i)]
(g) 78562 > 73946 because 7 = 7, but 8 > 3 [By rule (iii)]

(h) 96451 > 96279 because 96 = 96, but 4 > 2 [By rule (iii)]

Arranging Numbers in Ascending and Descending Order

When the numbers are arranged from the smallest to the largest, they are said to be in ascending order.
Arranging numbers from the largest to the smallest means arranging them in descending order.

For example: The numbers 1366, 2345, 52345, 52537, 65837, 70005 are arranged in ascending order and the
numbers 90022, 88798, 78041, 76966, 50102, 50048 are arranged in descending order.
3.6 LARGE NUMBERS ON A NUMBER LINE

A Number Line is a way to show numbers in order. Whole numbers can be shown on a number line, where
each point represents a whole number.
Draw a horizontal line and start at 0 on this line. The numbers increase as you move to the right.
Mark the points 1, 2, 3, 4, 5, 6, 7, 8, etc. on the line at equal distances to the right of 0. The distance between
0 and 1, 1 and 2, 2 and 3 and so on is 1 unit as shown below.
This line is known as the number line. 0 1 2 3 4 5 6 7 8
The arrow marks at both ends of the line indicate that it extends indefinitely in both directions.

Sometimes, we mark 0, 100, 200, 300, … at equal distances 198 525
to the right of 0 on the number line. In that case, the number 0 100 200 300 400 500 600 700 800

Number Play 67