Write down the decimal expansions of the following rational numbers by writing their denominators in the form of 2^m x 5^n, where m, and n, are the non-negative integers. (i) 3/8 (ii) 13/125 (iii) 7/80 (iv) 14588/625 (v) 129/(22 x 57)

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Write the Decimal Expansions of the Given Rational Numbers Video Explanation Watch the video below for the complete explanation: Solution Question: Write down the decimal expansions of the following rational numbers by writing their denominators in the form of 2m × 5n, where m and n are non-negative integers. Important Rule If the denominator of […]

Write down the decimal expansions of the following rational numbers by writing their denominators in the form of 2^m x 5^n, where m, and n, are the non-negative integers. (i) 3/8 (ii) 13/125 (iii) 7/80 (iv) 14588/625 (v) 129/(22 x 57) Read More »

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion. (i) 23/8 (ii) 125/441 (iii) 35/50 (iv) 77/210 (v) 129/(22 x 57 x 717) (vi) 987/10500

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Determine Whether the Given Rational Numbers Have Terminating or Non-Terminating Repeating Decimal Expansions Video Explanation Watch the video below for the complete explanation: Solution Question: Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion. Important Rule A rational number in

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion. (i) 23/8 (ii) 125/441 (iii) 35/50 (iv) 77/210 (v) 129/(22 x 57 x 717) (vi) 987/10500 Read More »

If p and q are prime positive integers, prove that √p + √q is an irrational number.

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Prove That √p + √q Is an Irrational Number Video Explanation Watch the video below for the complete explanation: Solution Statement: If p and q are prime positive integers, prove that √p + √q is an irrational number. Proof: Let us assume that √p + √q is a rational number. Then, squaring both sides, we

If p and q are prime positive integers, prove that √p + √q is an irrational number. Read More »

Prove that for any prime positive integer p, √p is an irrational number

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Prove That √p Is Irrational for Any Prime Positive Integer p Video Explanation Watch the video below for the complete explanation: Solution Statement: Prove that for any prime positive integer p, √p is an irrational number. Proof: Let us assume that √p is a rational number. Then we can write: √p = a / b

Prove that for any prime positive integer p, √p is an irrational number Read More »