Math, asked by anvi37, 1 year ago

without actual division show that 171 by 800 is a terminating decimal. express it in decimal form.


Tanya2208: You understood it??

Answers

Answered by hukam0685
12

Step-by-step explanation:

Given:

 \frac{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

 {2}^{n}  {5}^{m}  \\

where n and m are positive integers

800 = 8 \times 100 \\  \\ 800 = 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5 \\  \\ 800 =  {2}^{5}  \times  {5}^{2}  \\  \\

hence,

171/800 is having terminating decimal expansion.

To express in decimal form(without division)

 \frac{171}{800}   \\  \\ =  \frac{171}{ {2}^{5}  \times  {5}^{2} }  \\  \\  = \frac{171 \times  {5}^{3} }{ {2}^{5}  \times  {5}^{2}  \times  {5}^{3} }  \\  \\  =  \frac{171 \times  125 }{ {2}^{5}  \times  {5}^{5}  }  \\  \\  = \frac{21375 }{ {(10)}^{5}  } \\  \\  = \frac{21375 }{100000 } \\  \\ \bold{\frac{171}{800}   = 0.21375 }\\  \\

Hope it helps you.

To learn more on brainly:

1)Check whether

7/50

and

3/28

will have terminating decimal expansion or not

https://brainly.in/question/12302739

2)Which of the following has a terminating decimal expansion? (a) 32/91 (b) 19/80 (c) 23/45 (d) 25/42

https://brainly.in/question/8031357

Answered by charisma47
3

Answer:

171/800=0.21375.

is your answer

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