Page 93 - ICSE Math 6

Let’s represent 2.4 on the number line. Divide the line segment between 2 and 3 into 10 equal parts.
The fourth mark to the right of 2 shows 2.4.

2 2.4 3

Try These
1. The line segment between 5 and 6 on the number line is divided into 100 equal segments.
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What does the 6 mark to the right of 5 represent?
(a) 5.6 (b) 5.06 (c) 5.006 (d) 6
2. The line segment between –2 and –3 on the number line is divided into 1,000 equal parts.
Which mark represents –2.007?
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th
(a) 7 mark to the right –2 (b) 7 mark to the left of –2
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(c) 7 mark to the right of –3 (d) 7 mark to the left of –3
Example 1: Locate the decimals 0.3, 1.7, –2.5 and –0.8 on the number line.
Solution: Divide the line segment between 0 and 1 into ten equal parts. The third mark to the right
of 0 shows 0.3. Now, divide the line segment between 1 and 2 into ten equal parts. The
seventh mark to the right of 1 represents 1.7.

Similarly, to locate –2.5 and –0.8, divide the line segments between –2 and –3, and 0
and –1 into ten equal parts. The fifth mark to the left of –2 shows –2.5 and the eighth
mark to the left of 0 shows –0.8.

–2.5 –0.8 0.3 1.7
–3 –2 –1 0 1 2

Example 2: Between which two integers on the number line do the following decimals lie? Also,
write the integer nearest to the given decimals.
(a) 2.9 (b) –12.5 (c) 0.6 (d) –3.9
Solution: (a) 2.9 lies between 2 and 3. The integer nearest to 2.9 is 3.
(b) –12.5 lies between –13 and –12 and it is equidistant from –12 and –13.

(c) 0.6 lies between 0 and 1. The integer nearest to 0.6 is 1.
(d) –3.9 lies between –4 and –3. The integer nearest to –3.9 is –4.

Comparison of Decimals
While comparing decimals, the whole part is compared first and then the fractional part is compared.
The number with the greater whole part is bigger. If the whole parts are equal, then the decimal
number having a greater digit at the first decimal place is bigger. If the whole parts as well as the
digits at the first decimal place are equal, then the digits at the second decimal places are compared,
and so on.

Example 3: Which of the following is greater?
(a) 30.51 or 30.15 (b) 21.7 or 19.9
(c) 1.56 or 1.57 (d) 150.757 or 150.755
Solution: (a) 30.51 > 30.15 because 30 = 30 but 5 > 1.
(b) 21.7 > 19.9 because 21 > 19.
(c) 1.56 < 1.57 because 1 = 1 and 5 = 5 but 6 < 7.
(d) 150.757 > 150.755 because 150 = 150, 7 = 7 and 5 = 5 but 7 > 5.

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