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Question

Approximate 6 to two decimal places.

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Solution

Step 1: Find the whole number of the decimal form of 6 by perfect square method.

The largest perfect square less than 6 is 4.
The smallest perfect square greater than 6 is 9.

4 < 6 < 9
4 < 6 < 9
2 < 6 < 3

The whole number of decimal form of 6 lies between 2 and 3.

6 = 2._____

Step 2: Then, find the first decimal place of the decimal form of 6 by perfect square method. So, consider 600.

The largest perfect square less than 600 is 576.
The smallest perfect square greater than 6 is 625.

576 < 600 < 625
242 < 600 < 252 (242=576;252=625)

Now place the decimal point
5.76 < 6.00 < 6.25
2.42 < 6 < 2.52
2.42 < 6 < 2.52
2.4 < 6 <2.5

The first decimal place of 6 is 4.
6 = 2.4

Step 3: Then, find the second decimal place of the decimal form of 6 by perfect square method. So, consider 60,000.

The largest perfect square less than 60,000 is 59,536.
The smallest perfect square greater than 6 is 60,025.

59,536 < 60,000 < 60,025
2442 < 60,000 < 2452
(2442=59,536;2452=60,025)

Now place the decimal point
5.9536 < 6.0000 < 6.0025
2.442 < 6.0000 < 2.452
2.442 < 6 < 2.452
2.44 < 6 <2.45

The second decimal place of 6 is 4.
So we can write 6 as 2.44 .

The approximate value of 6 is 2.44.

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