Question

please answer me the two questions above
I'll be thankful ​

Answer 1

Answer

1.)( b)after three places of decimal .

$\frac{7}{20 \times 25} = > \frac{7}{500} = > 0.014$

2.)(a) terminating

$\frac{63}{72 \times 175} = > \frac{63}{ {2}^{3} \times 9 \times {5}^{2} \times 7 } = > \frac{1}{ {2}^{3} {5}^{2} } \\ \frac{1 \times 5}{ {2}^{3} {5}^{3} } = > \frac{5}{ {10}^{3} } = > \frac{5}{1000} = > 0.005$

0.005 is terminating

Answer 2

Note:

• Rational no : The number which can be written in the form of p/q where p and q are integers but q≠0 are called rational number .

Eg : 1/2 , 4/3 , 3.44 , 2.3333333....... etc

• Rational number can be characterized as;

1) Terminating

Eg : 1/2 , 3.44 , 5/4 etc

2) Non-terminating but repeating

( or Non-terminating but recurring )

Eg : 5/3 , 11/7 , 4.3333...... etc

• The rational number p/q (in its simplest form) will terminate if its denominator q can be written as 2^m × 5^n and its decimal expansion would terminate after m digits (ie, the power of 2) .

• The rational number (in its simplest form) whose denominator can't be written in the form 2^m×5^n has non-terminating but recurring decimal expansion.

• Irrational no. : All those numbers which are not rational are irrational numbers . Such type of number which cannot be written in the form of p/q where p and q are integers but q≠0 are called irrational number .

Eg : √3 , π , 3√2 , 1.207086499...... etc

• Irrational numbers are characterized as non-terminating non-recurring or non-terminating non-repeating .

Solution:

(Question 2)

The given rational number is :

7/(20×25) ie, 7/(2×2×5×5×5)

Clearly,

It is already in its simplest form.

Now,

The given rational number can be written as :

7/(2²×5³)

Here,

The denominator is 2²×5³

Clearly,

The denominator is of the form 2^m × 5^n ,

Where m = 2 and n = 3.

Thus,

The given rational number is terminating and its decimal expansion would terminates after 2 digits.

Hence,

The required answer is :

c) after two places of decimal.

Solution:

(Question 3)

The given rational number is :

63/(72×175) ie , (7×3×3)/(2×2×2×3×3×5×5×7)

The simplest form of the given rational number is;

1/(2×2×2×5×5)

Now,

The given rational number can be written as :

Here,

The denominator is 2³×5²

Clearly,

The denominator is of the form 2^m × 5^n ,

Where m = 3 and n = 2.

Thus,

The given rational number is terminating and its decimal expansion would terminates after 3 digits.

Hence,

The required answer is : a) terminating

Also refer to : https://brainly.in/question/16295517