Today our topic of discussion is Infinite decimal fractions.
Infinite decimal fractions
There are many decimal numbers that have infinitely many digits after decimal point. Moreover, a digit or a number of digits do not repeat as well. These are called infinite decimal fractions. For example, 5.134248513942301…is an infinite decimal fraction. Square root of 2 is an infinite decimal fraction. Let us calculate square root of 2.
In this way the procedure may continue indefinitely. So √2 1.4142135…is an = infinite decimal fraction.
Value and approximate values up to certain decimal point
It is not the same to calculate an infinite decimal fraction up to decimal places or approximate it to certain decimal places. For example, 5.4325893… when calculated up to 4 decimal places will give 5.4325 whereas its approximate value up to 4 decimal places will give us 5.4326.
However, these two values are same if we calculate up to 2 decimal places. We can do the same for finite decimal fractions as well.
Remarks: For finding values up to certain decimal places we must write down those digits exactly as they are. However, for finding approximation up to certain decimal places we need to check the next digit. If that digit is 5 or more, 1 should be added to the last position. Otherwise it will be kept in tact.
Example 21. Calculate values and approximate values of 4.4623845… up to 1, 2, 3, 4 and 5 decimal places ?
Solution: For the decimal fraction 4.4623845…
Value up to 1 decimal place is 4.4 but its approximate value up to 1 decimal digit is 4.5
Value up to 2 decimal places is 4.46 and approximate value is 4.46
Value up to 3 decimal places is 4.462 and approximate value is 4.462
Value up to 4 decimal places is 4.4623 and approximate value is 4.4624
Value up to 5 decimal places is 4.462238 and approximate value is 4.46238
Work: Calculate square root of 29 to 2 decimal places, and approximate it to 2 decimal places.
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