Question

State whether the following are terminating decimal expansion or a non terminating repeating decimal with out actual division 1)29÷343

Answer 1

non terminating as prime factorisation of denominator is not in form⬇
${2}^{m} \times {5}^{m}$

Answer 2

Hi there!
Here's the answer:

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Test for decimal expansion:

Method-1:
• Divide Numerator by denominator
• If Remainder is 0, the fraction is terminating decimal
• Else, if the remainders begin to repeat after some point, it is a non terminating Repeating (or) Recurring decimal

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29÷343 = 0.08454810496…

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Method-2:
• Express the fraction in lowest terms
(Can be done by dividing both Numerator and Denominator by their HCF)
• Resolve the denominator into prime factors
• If it contains only 2's or 5's or combination of both 2's and 5's, the fraction has a terminating decimal expansion.
• In all other cases, the fraction will have a repeating decimal expansion.

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Now,
(29/343)

• 343= 1 × 343, it is itself a prime. No factors other than one and itself.
•°• 343 is a non terminating repeating decimal.

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©#£€®$
:)
Hope it helps