Page 164 - Start Up Mathematics_6

Example 16: Between which two numbers in tenths place on the number line does each of the
given number lie?

(a) 0.99 (b) 0.67 (c) 0.01 (d) 0.18
Solution: (a) 0.99 lies between 0.9 and 1.0 (b) 0.67 lies between 0.6 and 0.7

(c) 0.01 lies between 0.0 and 0.1 (d) 0.18 lies between 0.1 and 0.2

Example 17: Write as fractions in the lowest term.
(a) 0.60 (b) 0.05 (c) 0.75 (d) 1.25

60 60 ÷ 20 3 5 55÷ 1
Solution: (a) 060. = = = (b) 005. = = =
100 100 ÷ 20 5 100 100 ÷ 5 20

75 75 ÷ 25 3 125 125 ÷ 25 5
(c) 075. = = = (d) 125. = = =
100 100 ÷ 25 4 100 100 ÷ 25 4

Comparison of Decimals

We use the following steps to compare two decimal numbers.
Step 1: Express the given decimals as like decimals.

Step 2: Compare the whole parts first. The number with the greater whole part is greater. If the
whole part of the numbers are equal then go to the next step (i.e., Step 3).

Step 3: Compare the tenths part, the decimal with the greater tenth digit is greater. If the tenth
part is also equal then compare the hundredths part and so on till you get a different part.

Example 18: Which is greater?
(a) 0.05 or 0.02 (b) 3.84 or 3.809 (c) 0.5 or 0.08 (d) 2.931 or 2.934
(e) 0.099 or 0.0158 (f) 3.4 or 3.40 (g) 2.814 or 2.821 (h) 8.8 or 8.800

Solution: (a) 0.05 and 0.02 are like decimals. The whole part of both the decimal numbers is
equal to 0.

Hence, we compare their tenths part which are also equal, i.e., 0 in both cases.

Now we compare the digits in their hundredth part;

Since 5 > 2, therefore 0.05 > 0.02.
(b) Expressing as like decimals, we get 3.840 and 3.809. The whole part of both
the decimal numbers is equal to 3.

Hence, we compare their tenths part which are also equal, i.e., 8 in both cases.

Now we compare the digits in their hundredth part.
Since 4 > 0, therefore 3.84 > 3.809.

Applying the steps discussed above we can show:

(c) 0.5 > 0.08 (d) 2.931 < 2.934 (e) 0.099 > 0.0158
(f) 3.4 = 3.40 (g) 2.814 < 2.821 (h) 8.8 = 8.800

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