Question

after how mañy decimal places will the decimal expression of 23/2⁴×5³ terminate

Answer 1

Answer:

4 decimal places

Step-by-step explanation:

For a number to be terminating, the denominator must be expressed in the powers of 2 and 5.

Now this denominator has powers of 2 and 5. But we must make sure that they both have the same powers.

If they dont have same powers, we must make sure that we must make them have same powers.

Now it is given that the denominator is 2⁴ × 5³

Now if we multiply 5 we get 5⁴

So multiplying 5 to both numerator and denominator we get,

⇒ ( 23 × 5 ) / ( 2⁴ × 5³ × 5 )

⇒ ( 115 ) / ( 2⁴ × 5⁴ )

We know that if two numbers have common powers in multiplication, we can multiply their bases.

Hence 2⁴ ×5⁴ can be written as : ( 2 × 5 )⁴ = 10⁴

⇒ 115 / 10⁴

⇒ 115 / 10000 = 0.0115

Hence it will terminate after 4 decimal places.

Hope it helped !!

Answer 2

Answer:

Step-by-step explanation:Here the given no. Is 23/16×125

We know that it is a terminating decimal expression as it contains only the factors 2 and 5. If we evaluate 16×125 it becomes 2000 and divide 23 by 2000, we get 0.0115

By following the long division method, we get that this number terminate after 4

Decimal places.

Alternative method:

By observing the highest degree among 2 and 5 factors .

In this no., 2 has the exponent 4 and 5 has the exponent 3,as 4>3 ,so the highest degree of 2 determine the decimal place. Here the no. repeates after 4 decimal places.