Question

after how many decimal expansion will 15/1600 terminate​

Answer 1

$\frac{15}{1600} = \frac{15}{ {2}^{6} \times {5}^{2} }$

Here, the greatest power is 6 (2^6)

Hence,

the fraction will terminate after $\red{\huge{6}}$ places

Answer 2

Answer:

The decimal expansion of the given rational number is 0.009375.

Step-by-step explanation:

Given a rational number,

$\dfrac{15}{1600}$

• To write the rational number in decimal expansion form, convert the rational number into a decimal fraction.  
• Decimal fraction is the one that has the powers of 10 in the denominator namely 10, 100, 1000 etc.

In the given rational number, the number in the denominator is 1600.

The next power of 10 to 1600 would be 10000.

But dividing 10000  by 1600 leaves a decimal, therefore choose 1000000 and divide, so that $\dfrac{1000000}{1600} =625$

Thus, to convert 1600 to 1000000, need to multiply 1600 with 625.

Thus, multiplying and dividing the given rational number by 625, we get

$\dfrac{15\times 625}{1600\times 625} =\dfrac{9375}{1000000}$

Now there are 6 zeroes in the denominator, so from right side count 6 digits, put the decimal point.

There are only 4 digits in the numerator, to make 6 digits put 2 zeroes before and place the decimal point.

$\dfrac{9375}{1000000}=0.009375$

Hence, the decimal expansion of the given rational number is 0.009375.