Question

Write the following rational numbers in the form of p/q, where q is of the form 2ⁿ .5^m where n, m are non-negative integers and then write the numbers in their decimal form.

i) \(\frac{3}{4}\)

ii) \(\frac{7}{25}\)

iii) \(\frac{51}{64}\)

iv) \(\frac{14}{25}\)

v) \(\frac{80}{100}\)

Answer 1

i) \(\frac{3}{4}\)

\(\frac{3}{4}\) = \(\frac{3}{2*2}\) = \(\frac{3}{2^2}\)

Decimal form of \(\frac{7}{25}\) = 0.28

ii) \(\frac{7}{25}\)

\(\frac{7}{25}\) = \(\frac{7}{5*5} = \frac{7}{5^2}\)

Decimal form of \(\frac{7}{25}\)= 0.28

iii) \(\frac{51}{64}\)

\(\frac{51}{64}=\frac{51}{2^6}\)

[ ∵ 64 = 2 × 32

= 2² x 16

= 2³ x 8

=2⁴ x 4 

=2⁵  x 2

=2^{6 ]}

Decimal form of \(\frac{51}{64}\)= 0.796875

iv) \(\frac{14}{25}\)

v) \(\frac{80}{100}\)

\(\frac{80}{100}=\frac{80}{2^2*5^2}=\frac{80}{10^2}=0.80\)