Question

Write the following rational in decimal form using theorem 1.2
1. 13/25. 2. 15/16. 3. 23/200
4. 7218/225. 5. 143/110​

Answer 1

$\red{ 1. \frac{13}{25}}$

$= \frac{13}{5^{2}}$

$\blue{( Denominator \:is \: of \:the \: form \: 2^{n}5^{m} )}$

$= \frac{13\times 2^{2}}{5^{2} \times 2^{2}}$

$= \frac{13 \times 4}{(5 \times 2)^{2}}$

$= \frac{52}{10^{2}}$

$= \frac{52}{100}$

$= 0.52 \: \green { ( Terminating \: Decimal )}$

$\red{ 2. \frac{15}{16}}$

$= \frac{15}{2^{4}}$

$\blue{( Denominator \:is \: of \:the \: form \: 2^{n}5^{m} )}$

$= \frac{15\times 5^{4}}{5^{4} \times 2^{4}}$

$= \frac{15 \times 625}{(5 \times 2)^{4}}$

$= \frac{9375}{10^{4}}$

$= \frac{9375}{10000}$

$= 0.9375\: \green { ( Terminating \: Decimal )}$

$\red{ 3. \frac{23}{200}}$

$= \frac{23}{2^{3}\times 5^{2}}$

$\blue{( Denominator \:is \: of \:the \: form \: 2^{n}5^{m} )}$

$= \frac{23\times 5}{5^{3} \times 2^{3}}$

$= \frac{23 \times 5}{(5 \times 2)^{3}}$

$= \frac{115}{10^{3}}$

$= \frac{115}{1000}$

$= 0.115\: \green { ( Terminating \: Decimal )}$

$\red{ 4. \frac{7218}{225}}$

$= \frac{ 9 \times 802}{9 \times 25}$

$= \frac{ 802}{25}$

$= \frac{802}{5^{2}}$

$\blue{( Denominator \:is \: of \:the \: form \: 2^{n}5^{m} )}$

$= \frac{802\times 2^{2}}{5^{2} \times 2^{2}}$

$= \frac{802 \times 4}{(5 \times 2)^{2}}$

$= \frac{3208}{10^{2}}$

$= \frac{3208}{100}$

$= 32.08\: \green { ( Terminating \: Decimal )}$

$\red{ 5. \frac{143}{110}}$

$= \frac{ 11 \times 13}{11 \times 10}$

$= \frac{ 13}{10}$

$= \frac{13}{5^{1}\times 2^{1}}$

$\blue{( Denominator \:is \: of \:the \: form \: 2^{n}5^{m} )}$

$= 1.3\: \green { ( Terminating \: Decimal )}$

•••♪

Answer 2

Step-by-step explanation:

\red{ 1. \frac{13}{25}}1.

25

13

= \frac{13}{5^{2}}=

5

2

13

\blue{( Denominator \:is \: of \:the \: form \: 2^{n}5^{m} )}(Denominatorisoftheform2

n

5

m

)

= \frac{13\times 2^{2}}{5^{2} \times 2^{2}}=

5

2

×2

2

13×2

2

= \frac{13 \times 4}{(5 \times 2)^{2}}=

(5×2)

2

13×4

= \frac{52}{10^{2}}=

10

2

52

= \frac{52}{100}=

100

52

= 0.52 \: \green { ( Terminating \: Decimal )}=0.52(TerminatingDecimal)

\red{ 2. \frac{15}{16}}2.

16

15

= \frac{15}{2^{4}}=

2

4

15

\blue{( Denominator \:is \: of \:the \: form \: 2^{n}5^{m} )}(Denominatorisoftheform2

n

5

m

)

= \frac{15\times 5^{4}}{5^{4} \times 2^{4}}=

5

4

×2

4

15×5

4

= \frac{15 \times 625}{(5 \times 2)^{4}}=

(5×2)

4

15×625

= \frac{9375}{10^{4}}=

10

4

9375

= \frac{9375}{10000}=

10000

9375

= 0.9375\: \green { ( Terminating \: Decimal )}=0.9375(TerminatingDecimal)

\red{ 3. \frac{23}{200}}3.

200

23

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

2

3

×5

2

23

\blue{( Denominator \:is \: of \:the \: form \: 2^{n}5^{m} )}(Denominatorisoftheform2

n

5

m

)

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

5

3

×2

3

23×5

= \frac{23 \times 5}{(5 \times 2)^{3}}=

(5×2)

3

23×5

= \frac{115}{10^{3}}=

10

3

115

= \frac{115}{1000}=

1000

115

= 0.115\: \green { ( Terminating \: Decimal )}=0.115(TerminatingDecimal)

\red{ 4. \frac{7218}{225}}4.

225

7218

= \frac{ 9 \times 802}{9 \times 25}=

9×25

9×802

= \frac{ 802}{25}=

25

802

= \frac{802}{5^{2}}=

5

2

802

\blue{( Denominator \:is \: of \:the \: form \: 2^{n}5^{m} )}(Denominatorisoftheform2

n

5

m

)

= \frac{802\times 2^{2}}{5^{2} \times 2^{2}}=

5

2

×2

2

802×2

2

= \frac{802 \times 4}{(5 \times 2)^{2}}=

(5×2)

2

802×4

= \frac{3208}{10^{2}}=

10

2

3208

= \frac{3208}{100}=

100

3208

= 32.08\: \green { ( Terminating \: Decimal )}=32.08(TerminatingDecimal)

\red{ 5. \frac{143}{110}}5.

110

143

= \frac{ 11 \times 13}{11 \times 10}=

11×10

11×13

= \frac{ 13}{10}=

10

13

= \frac{13}{5^{1}\times 2^{1}}=

5

1

×2

1

13

\blue{( Denominator \:is \: of \:the \: form \: 2^{n}5^{m} )}(Denominatorisoftheform2

n

5

m

)

= 1.3\: \green { ( Terminating \: Decimal )}=1.3(TerminatingDecimal)

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