Write down the decimal expansion of the following rational numbers by writing the denominators in the form 2m-5n- where m-n are non-negative integers-i 3 8 ii 13 125 iii 7 80 iv 14588 625 v 129 2 2 - 5 7

(i) #160; 3 8 =( 3 2 ^ 3 #160; )=0.375 , #160; #160; #160; #160; #160;(ii) #160; 13 125 = 13 5 ^ 3 =0.104 (iii) #160; ...

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Standard X

Mathematics

Check If a Given Rational No. Is Terminating or Not

Write down th...

Question

Write down the decimal expansion of the following rational numbers by writing the denominators in the form $2^{m} \times 5^{n}$ , where $m, n$ are non-negative integers.
(i) $\frac{3}{8}$ (ii) $\frac{13}{125}$ (iii) $\frac{7}{80}$ (iv) $\frac{14588}{625}$ (v) $\frac{129}{2^{2} \times 5^{7}}$

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Solution

(i) $\frac{3}{8} = (\frac{3}{2^{3}}) = 0.375$ ,

(ii) $\frac{13}{125} = \frac{13}{5^{3}} = 0.104$

(iii) $\frac{7}{80} = \frac{7}{2^{4} \times 5} = 0.0875$ ,
(iv) $\frac{14588}{625} = \frac{14588}{5^{4}} = 23.34$

(v) $\frac{129}{2^{2} \times 5^{7}} = 4.128 \times 10^{- 4}$

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Similar questions

Q. Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2^m × 5ⁿ, where, m, n are non-negative integers.

(i)

\frac{3}{8}

(ii)

\frac{13}{125}

(iii)

\frac{7}{80}

(iv)

\frac{14588}{625}

(v)

\frac{129}{2^{2} \times 5^{7}}

[NCERT]

Question 13
Write the denominator of rational number $\frac{257}{5000}$ in the form $2^{m} \times 5^{n}$ , where m, n are non - negative integers. Hence, write its decimal expansion, without actual division.

Q. Write the denominator of the rational number

\frac{257}{5000}

in the form

2^{m} \times 5^{n}

, where

m, n

are non-negative integers. Hence, write the decimal expansion, without actual division.

Q. 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)

\frac{23}{8}

(ii)

\frac{125}{441}

(iii)

\frac{35}{50}

(iv)

\frac{77}{210}

(v)

\frac{129}{2^{2} \times 5^{7} \times 7^{17}}

Q. Write down the decimal expansions of the rational numbers which have terminating decimal expansions.
(i)

\frac{13}{3125}

(ii)

\frac{17}{8}

(iii)

\frac{15}{1600}

(iv)

\frac{23}{2^{3} 5^{2}}

(v)

\frac{6}{15}

(vi)

\frac{35}{50}

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Write down the decimal expansion of the following rational numbers by writing the denominators in the form 2m×5n, where m,n are non-negative integers.(i) 38 (ii) 13125 (iii) 780 (iv) 14588625 (v) 12922×57

(i) 38=(323)=0.375 , (ii) 13125=1353=0.104(iii) 780=724×5=0.0875 , (iv) 14588625=1458854=23.34(v) 12922×57=4.128×10−4

Write down the decimal expansion of the following rational numbers by writing the denominators in the form $2^{m} \times 5^{n}$ , where $m, n$ are non-negative integers.
(i) $\frac{3}{8}$ (ii) $\frac{13}{125}$ (iii) $\frac{7}{80}$ (iv) $\frac{14588}{625}$ (v) $\frac{129}{2^{2} \times 5^{7}}$

(i) $\frac{3}{8} = (\frac{3}{2^{3}}) = 0.375$ ,

(ii) $\frac{13}{125} = \frac{13}{5^{3}} = 0.104$

(iii) $\frac{7}{80} = \frac{7}{2^{4} \times 5} = 0.0875$ ,
(iv) $\frac{14588}{625} = \frac{14588}{5^{4}} = 23.34$

(v) $\frac{129}{2^{2} \times 5^{7}} = 4.128 \times 10^{- 4}$