Question

Write the following rational numbers in their decimal form and also state which are terminating and which have non-terminating repeating decimals.

i) \(\frac{3}{8}\)

ii) \(\frac{229}{400}\)

iii) 4\(\frac{1}{5}\)

iv)\(\frac{2}{11}\)

v) \(\frac{8}{125}\)

Answer 1

i) \(\frac{3}{8}\)

[!! Denominator 8 = 2³, consists of only 2’s. Hence a terminating decimal.] 

∴ \(\frac{3}{8}\)= 0.375 is a terminating decimal.

ii) \(\frac{229}{400}\)

[!! Denominator 400 = 2⁴ × 5² = 2ⁿ × 5^m . Hence a terminating decimal.] 

∴ \(\frac{229}{400}\)= 0.5725 is a terminating decimal.

iii) \(4\frac{1}{5}\)

\(4\frac{1}{5}\) = 4 + \(\frac{1}{5}\)

[!! Denominator is 5. Hence a terminating decimal.] 

∴ 4\(\frac{1}{5}\) = 4.2 is a terminating decimal.

iv) \(\frac{2}{11}\)

[!! Denominator is not of the form 2^m × 5ⁿ . Hence a non-terminating repeating decimal.] 

∴ \(\frac{2}{11}\)= \(0.\overline{18}\) is a non terminating, repeating decimal.

v) \(\frac{8}{125}\)

[!! Denominator 125 = 5³ . Hence a terminating decimal.] 

∴ \(\frac{8}{125}\)= 0.064 is a terminating decimal.