Question

evaluate decimal expansion of -16/45​

Answer 1

Answer:

Answer:

\frac{46}{2^{2}\times 5^{3}}= 0.092

2

2

×5

3

46

=0.092

Step-by-step explanation:

\frac{46}{2^{2}\times 5^{3}}

2

2

×5

3

46

\begin{lgathered}Denominator \: is \:of \:form \:2^{n}\times 5^{m}.\\It \:is \: a \: terminating \: decimal\end{lgathered}

Denominatorisofform2

n

×5

m

.

Itisaterminatingdecimal

\frac{46}{2^{2}\times 5^{3}}=\frac{46\times 2}{2^{3}\times 5^{3}}

2

2

×5

3

46

=

2

3

×5

3

46×2

=\frac{92}{(2\times 5)^{3}}=

(2×5)

3

92

=\frac{92}{(10)^{3}}=

(10)

3

92

=\frac{92}{1000}=

1000

92

=0.092=0.092

/* Terminating decimal */

Therefore,

\frac{46}{2^{2}\times 5^{3}}= 0.092

2

2

×5

3

46

=0.092

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