Page 51 - Start Up Mathematics_7

Solution: (a) Place value of 2 in 32.56 is 2.

(b) Place value of 2 in 23.87 is 20.
(c) Place value of 2 in 10.24 is two tenths, i.e., .2
(d) Place value of 2 in 71.112 is two thousandths, i.e., .002.

Decimal places
The number of decimal places is the number of digits on the right of the decimal point. For example,
the number of decimal places in 27.834 is 3.

Like decimals
The decimals having the same number of decimal places are called like decimals. Examples of
like decimals are 131.8 and 24.2; 0.718 and 5,112.101.

Unlike decimals

The decimals having different number of decimal places are called unlike decimals. For example,
12.5, 12.52 and 12.527 are unlike decimals.

Unlike decimals like 0.5, 0.50, 0.500 are equal as writing or removing zeros at the extreme right of the
decimals does not change its value.

Comparison of Decimals
For comparing two decimal numbers, we follow the given steps:

Step 1: Compare the whole parts first. The number having the greater whole part is greater. If
the whole part is same, proceed to step 2.
Step 2: Compare the tenth parts of the decimals. The number having the greater tenth part is
greater. If the tenth part is same, proceed to step 3.

Step 3: Compare their hundredth parts and so on, till one of them is different. The number having
the first greater part is greater.
Example 3: Which is greater?

(a) 14.998 or 15.001 (b) 3.02 or 3.20 (c) 2.684 or 2.681
Solution: (a) 14.998 or 15.001

We first compare the whole numbers on the left of the decimal point. Since
14 < 15 therefore 14.998 < 15.001.
(b) 3.02 or 3.20

We first compare the digit on the left of the decimal point. Here both the digits
are same, i.e., 3. So we compare the digit on the right of the decimal point
starting from the tenths place. We find 0 < 2, therefore 3.02 < 3.20.

(c) 2.684 or 2.681
We first compare their whole parts, which are same, i.e., 2. Now we compare
their tenths part, which are also same, i.e., 6. Next we compare their hundredths
part which are also same, i.e., 8. The difference is in their thousandth parts, i.e.,
4 > 1, therefore 2.684 > 2.681.

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