Question

171/800 find answer without division with step by step explanation​

Answer 1

Answer:

171/800

= To find :Without actual division show that 171 by 800 is a terminating decimal. express it in decimal form.

Solution:

To show that 171/800 is terminating,

find the prime factors of 800,If it is in the form

2n 5m

where n and m are positive integers

800 = 8 × 100

800 = 2 × 2× 2 × 2 × 2 × 5 × 5

800 = 2⁵ × 5²

hence,

171/800 is having terminating decimal expansion.

To express in decimal form(without division)

171/800

= 171/2⁵ × 5²

= 171 × 5³ / 2⁵ × 5²× 5³

= 171 ×125 / 2⁵ × 5⁵

= 21375/ (10)²

= 0.21375

Step-by-step explanation:

I hope it's helpful for you