Question

a)The decimal expansion of 18

3750

will terminate after how many decimal places?​

Answer 1

Step-by-step explanation:

We know that a terminating decimal is a decimal that ends. It's a decimal with a finite number of digits. For example

4

1

=0.25, it has only two decimal digits.

Now consider the fraction

32

5

whose decimal form will be:

32

5

=0.15625

The resulting decimal number ends with five decimal digits and therefore, it is terminating decimal.

Hence,

32

5

has a terminating decimal expansion.

While,

9

7

=0.7777..., non-terminating,

15

8

=0.5333..., non-terminating

and

9

7

=0.08333..., non-terminating

Therefore, option A is correct

Answer 2

Answer:

The decimal expansion of $\frac{18}{3750}$ is 0.0048 and it will terminates 4 decimal places

Step-by-step explanation:

Given : The decimal expansion  $\frac{18}{3750}$

To find: Decimal place of termination in the decimal expansion.

Decimal expansion:

• The representation of a number with a decimal point either real or assumed called a decimal expansion.
• The base-10 representation of a number is its decimal expansion.
• Each "decimal place" in this system is made up of a digit 0–9 that is multiplied by a power of 10 in decreasing order from left to right with the decimal place.
• After a certain number of steps, the decimal expansion comes to a conclusion. It's referred to as terminating decimal.

Simplify the given values $\frac{18}{3750}$

$\frac{18}{3750} = 0.0048$

We can take the digits after the decimal point. There are four places of decimal.

Hence it will terminates 4 places of decimal.

Final answer:

The decimal expansion of $\frac{18}{3750}$ is 0.0048 and it will terminates 4 decimal places

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