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mina [271]
3 years ago
12

Estimate the value of the irrational number (0.6289731...)2. Up to how many decimal digits is the estimation correct? 4 5 6 7

Mathematics
2 answers:
Salsk061 [2.6K]3 years ago
8 0

Answer:

7 decimal digits

Step-by-step explanation:

Because it ws rounded up to 0.6289731

and the known digits after the decimal are 7 in numbers.

0.6290 ......4 decimal digits

0.62897..... 5 decimal digits

0.628973.... 6 decimal digits

0.628973 ..... 7 decimal digits

Mademuasel [1]3 years ago
3 0

Answer:

0.927

Step-by-step explanation:

The value can be estimated using the binomial theorem for expanding numbers. The theorem states:

For an expansion

(1+x)^{n}  = 1+ \frac{n}{1}x+\frac{n(n-1)}{1*2} x^{2}  + ...

Now, let's take the value 0.6289731. In the expression, let 0.6289731 be equal to ( 1 - 0.0371)

We can use the binomial expansion above:

(1-0.0371)^{2}  = 1+ (-)\frac{(2)}{1} (0.0371) + \frac{2(2-1)}{1*2} (-0.0371)^{2}  + ... up to three terms

This gives 1-0.0734+0.00137641 = 0.927 up to 3 decimal places

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