Question

the decimal expansion of the sum of rational number 15/4 and 23/40 will be terminate after​

Answer 1

Given,

Rational numbers = $\[\frac{{15}}{4},\frac{{23}}{{40}}\]$

Solution,

Calculate the sum of rational numbers,

$\[ = \frac{{15}}{4} + \frac{{23}}{{40}}\]$

$\[ = \frac{{15 \times 10}}{{4 \times 10}} + \frac{{23}}{{40}}\]$

$\[ = \frac{{150}}{{40}} + \frac{{23}}{{40}}\]$

$\[ = \frac{{173}}{{40}}\]$

$\[ = 4.325\]$

Hence the decimal expression of sum of rational numbers will be terminate after 3 digits.

Answer 2

Given :   15/4 + 23/40

To Find :   decimal expansion of the sum  will be terminate after​

Solution:

15/4 + 23/40

Taking LCM 40

= (150 + 23)/40

= 173/40

173 is prime number

40  = 2 * 2 * 2 * 5

=> 40 = 2³ * 5¹

Hence will terminate after 3 decimal places

173/40  = 173 * 5 * 5/ (40 * 5 * 5)

= 4325 / (1000)

= 4.325

terminate after 3 decimal places

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