Question

After how many places of decimal will the decimal expansion of 147/120 terminate?

Answer 1

Answer:

3 decimal places.

Step-by-step explanation:

Given : Number $\frac{147}{120}$

To find : After how many places of decimal will the decimal expansion of number terminate?

Solution :

The prime factorization of numerator and denominator is

$147=3\times 7\times 7$

$120=2\times 2\times 2\times 3\times 5$

$\frac{147}{120}=\frac{3\times 7\times 7}{2\times 2\times 2\times 3\times 5}$

Eliminate the 3 from numerator and denominator.

$\frac{147}{120}=\frac{7\times 7}{2\times 2\times 2\times 5}$

The power of 2 in the denominator gives u the number of decimal terminate.

The power of 2 is $2^3$

The places of decimal will the decimal expansion is 3 places.

$\frac{147}{120}=1.225$

Answer 2

Answer:

Decimal place come after one digit .

Step-by-step explanation:

$Given\\\frac{147}{120}=\frac{3\times 49}{3\times 40}=\frac{49}{40}$

$Denominator \: (q)= 40=2^{3}\times 5$

$q \: of \: the \: form \: 2^{n}\times 5^{m}$

Therefore,

$\frac{147}{120} \: is \: a \: terminating\: decimal$

$\frac{147}{120}=\frac{49}{40}\\=\frac{49}{2^{3}\times 5}\\=\frac{49\times 5^{2}}{2^{3}\times 5^{3}}\\=\frac{1225}{(10^{3})}\\=\frac{1225}{1000}\\=1.225$

Therefore,

Decimal place come after one digit .

•••♪