# Number - Decimals to Fractions

**Question 1**

Convert the following decimals to fractions

a) $0.1$

a
$\frac{1}{10}$

Question ID: 10220010010

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b) $0.3$

a
$\frac{3}{10}$

Question ID: 10220010020

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c) $0.7$

a
$\frac{7}{10}$

Question ID: 10220010030

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d) $0.9$

a
$\frac{9}{10}$

Question ID: 10220010040

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**Question 2**

Convert the following decimals to simplified fractions

a) $0.5$

a
$\frac12$

Question ID: 10220020010

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b) $0.2$

a
$\frac15$

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c) $0.4$

a
$\frac25$

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d) $0.6$

a
$\frac35$

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**Question 3**

Convert the following decimals to fractions

a) $0.13$

a
$\frac{13}{100}$

Question ID: 10220030010

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b) $0.23$

a
$\frac{23}{100}$

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c) $0.99$

a
$\frac{99}{100}$

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d) $0.01$

a
$\frac{1}{100}$

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e) $0.09$

a
$\frac{9}{100}$

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f) $0.33$

a
$\frac{33}{100}$

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**Question 4**

Convert the following decimals to simplified fractions

a) $0.25$

a
$\frac14$

Question ID: 10220040010

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b) $0.02$

a
$\frac{1}{50}$

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c) $0.05$

a
$\frac{1}{20}$

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d) $0.04$

a
$\frac{1}{25}$

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**Question 5**

Convert the following decimals to simplified fractions

a) $0.75$

a
$\frac34$

Question ID: 10220050010

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b) $0.15$

a
$\frac{3}{20}$

Question ID: 10220050020

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c) $0.35$

a
$\frac{7}{20}$

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d) $0.55$

a
$\frac{11}{20}$

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e) $0.06$

a
$\frac{3}{50}$

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f) $0.08$

a
$\frac{2}{25}$

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**Question 6**

Convert the following decimals to simplified fractions

a) $0.34$

a
$\frac{17}{50}$

Question ID: 10220060010

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b) $0.45$

a
$\frac{9}{20}$

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c) $0.54$

a
$\frac{27}{50}$

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d) $0.76$

a
$\frac{19}{25}$

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e) $0.62$

a
$\frac{31}{50}$

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f) $0.88$

a
$\frac{22}{25}$

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**Question 7**

Convert the following decimals to fractions

a) $0.123$

a
$\frac{123}{1000}$

Question ID: 10220070010

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b) $0.533$

a
$\frac{533}{1000}$

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c) $0.003$

a
$\frac{3}{1000}$

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d) $0.063$

a
$\frac{63}{1000}$

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**Question 8**

Convert the following decimals to simplified fractions

a) $0.002$

a
$\frac{1}{500}$

Question ID: 10220080010

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b) $0.005$

a
$\frac{1}{200}$

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c) $0.008$

a
$\frac{1}{125}$

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d) $0.006$

a
$\frac{3}{500}$

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e) $0.004$

a
$\frac{2}{500}$

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**Question 9**

Convert the following decimals to simplified fractions

a) $0.122$

a
$\frac{61}{500}$

Question ID: 10220090010

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b) $0.586$

a
$\frac{293}{500}$

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c) $0.075$

a
$\frac{3}{40}$

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d) $0.672$

a
$\frac{84}{125}$

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e) $0.455$

a
$\frac{91}{200}$

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f) $0.095$

a
$\frac{19}{200}$

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**Question 10**

Convert the following decimals to fractions

a) $0.1733$

a
$\frac{1733}{10000}$

Question ID: 10220100010

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b) $0.8237$

a
$\frac{8237}{10000}$

Question ID: 10220100020

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c) $0.5051$

a
$\frac{5051}{10000}$

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d) $0.0007$

a
$\frac{7}{10000}$

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e) $0.0403$

a
$\frac{403}{10000}$

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f) $0.1823$

a
$\frac{1823}{10000}$

Question ID: 10220100060

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**Question 11**

Convert the following decimals to simplified fractions

a) $0.4842$

a
$\frac{2421}{5000}$

Question ID: 10220110010

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b) $0.8215$

a
$\frac{1643}{2000}$

Question ID: 10220110020

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c) $0.2108$

a
$\frac{527}{2500}$

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d) $0.0096$

a
$\frac{6}{625}$

Question ID: 10220110040

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e) $0.0008$

a
$\frac{1}{1250}$

Question ID: 10220110050

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f) $0.0905$

a
$\frac{161}{2000}$

Question ID: 10220110060

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**Question 12**

Convert the following decimals to fractions. Leave your answers as mixed numbers

a) $1.5$

a
$1\frac12$

Question ID: 10220120010

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b) $3.7$

a
$3\frac{7}{10}$

Question ID: 10220120020

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c) $2.2$

a
$2\frac15$

Question ID: 10220120030

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d) $9.25$

a
$9\frac14$

Question ID: 10220120040

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e) $3.125$

a
$3\frac18$

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f) $8.0625$

a
$8\frac{1}{16}$

Question ID: 10220120060

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**Question 13**

Convert the following decimals to fractions. Leave your answers as improper fractions

a) $3.5$

a
$\frac72$

Question ID: 10220130010

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b) $1.3$

a
$\frac{13}{10}$

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c) $4.2$

a
$\frac{21}{5}$

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d) $8.25$

a
$\frac{33}{4}$

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e) $1.125$

a
$\frac98$

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f) $2.0625$

a
$\frac{33}{16}$

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**Question 14**

Convert the following decimals to fractions. Leave your answers as mixed numbers, simplifying where necessary.

a) $3.6$

a
$3\frac35$

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b) $2.8$

a
$2\frac45$

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c) $4.75$

a
$4\frac34$

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d) $1.04$

a
$1\frac{1}{25}$

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e) $10.875$

a
$10\frac78$

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f) $1.8125$

a
$1\frac{13}{16}$

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**Question 15**

Convert the following decimals to fractions. Leave your answers as improper fractions, simplifying where necessary.

a) $1.4$

a
$\frac75$

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b) $2.75$

a
$\frac{11}{4}$

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c) $3.8$

a
$\frac{19}{5}$

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d) $3.375$

a
$\frac{27}{8}$

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e) $1.05$

a
$\frac{21}{20}$

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f) $2.3125$

a
$\frac{37}{16}$

Question ID: 10220150060

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**Question 16**

Convert the following decimals to fractions. Leave your answers as mixed numbers, simplifying where necessary.

a) $6.15$

a
$6\frac{3}{20}$

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b) $1.22$

a
$1\frac{11}{50}$

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c) $3.85$

a
$3\frac{17}{20}$

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d) $2.84$

a
$2\frac{21}{25}$

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e) $9.142$

a
$9\frac{71}{500}$

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f) $8.0205$

a
$8\frac{41}{2000}$

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**Question 17**

Convert the following decimals to fractions. Leave your answers as improper fractions, simplifying where necessary.

a) $3.45$

a
$\frac{69}{20}$

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b) $1.88$

a
$\frac{47}{25}$

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c) $5.505$

a
$\frac{1101}{200}$

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d) $10.032$

a
$\frac{1254}{125}$

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e) $5.132$

a
$\frac{1283}{250}$

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f) $2.8424$

a
$\frac{3553}{1250}$

Question ID: 10220170060

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**Question 18**

Convert the following decimals to simplified fractions

a) $0.\dot{3}$

a
$\frac13$

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b) $0.\dot{6}$

a
$\frac23$

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c) $0.\dot{1}$

a
$\frac19$

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d) $0.\dot{2}$

a
$\frac29$

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e) $0.\dot{5}$

a
$\frac59$

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f) $0.\dot{8}$

a
$\frac89$

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g) $0.1\dot{6}$

a
$\frac16$

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h) $0.8\dot{3}$

a
$\frac56$

Question ID: 10220180080

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i) $0.\dot{0}\dot{9}$

a
$\frac{1}{11}$

Question ID: 10220180090

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j) $0.\dot{1}\dot{8}$

a
$\frac{2}{11}$

Question ID: 10220180100

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k) $0.\dot{4}\dot{5}$

a
$\frac{5}{11}$

Question ID: 10220180110

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l) $0.\dot{9}\dot{0}$

a
$\frac{10}{11}$

Question ID: 10220180120

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**Question 19**

Answer the following:

a) Convert $0.\dot{9}$ to a fraction. Explain your answer.

a
If $0.\dot{3}=\frac13$ and $0.\dot{6}=\frac23$

Then $0.\dot{9}=\frac33$

However $\frac33=1$.

You have shown that $0.999999\dots=1$

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If $0.\dot{3}=\frac13$ and $0.\dot{6}=\frac23$

Then $0.\dot{9}=\frac33$

However $\frac33=1$.

You have shown that $0.999999\dots=1$

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**Question 1**

Convert the following decimals to fractions

a) $0.1$

b) $0.3$

c) $0.7$

d) $0.9$

**Question 2**

Convert the following decimals to simplified fractions

a) $0.5$

b) $0.2$

c) $0.4$

d) $0.6$

**Question 3**

Convert the following decimals to fractions

a) $0.13$

b) $0.23$

c) $0.99$

d) $0.01$

e) $0.09$

f) $0.33$

**Question 4**

Convert the following decimals to simplified fractions

a) $0.25$

b) $0.02$

c) $0.05$

d) $0.04$

**Question 5**

Convert the following decimals to simplified fractions

a) $0.75$

b) $0.15$

c) $0.35$

d) $0.55$

e) $0.06$

f) $0.08$

**Question 6**

Convert the following decimals to simplified fractions

a) $0.34$

b) $0.45$

c) $0.54$

d) $0.76$

e) $0.62$

f) $0.88$

**Question 7**

Convert the following decimals to fractions

a) $0.123$

b) $0.533$

c) $0.003$

d) $0.063$

**Question 8**

Convert the following decimals to simplified fractions

a) $0.002$

b) $0.005$

c) $0.008$

d) $0.006$

e) $0.004$

**Question 9**

Convert the following decimals to simplified fractions

a) $0.122$

b) $0.586$

c) $0.075$

d) $0.672$

e) $0.455$

f) $0.095$

**Question 10**

Convert the following decimals to fractions

a) $0.1733$

b) $0.8237$

c) $0.5051$

d) $0.0007$

e) $0.0403$

f) $0.1823$

**Question 11**

Convert the following decimals to simplified fractions

a) $0.4842$

b) $0.8215$

c) $0.2108$

d) $0.0096$

e) $0.0008$

f) $0.0905$

**Question 12**

Convert the following decimals to fractions. Leave your answers as mixed numbers

a) $1.5$

b) $3.7$

c) $2.2$

d) $9.25$

e) $3.125$

f) $8.0625$

**Question 13**

Convert the following decimals to fractions. Leave your answers as improper fractions

a) $3.5$

b) $1.3$

c) $4.2$

d) $8.25$

e) $1.125$

f) $2.0625$

**Question 14**

Convert the following decimals to fractions. Leave your answers as mixed numbers, simplifying where necessary.

a) $3.6$

b) $2.8$

c) $4.75$

d) $1.04$

e) $10.875$

f) $1.8125$

**Question 15**

Convert the following decimals to fractions. Leave your answers as improper fractions, simplifying where necessary.

a) $1.4$

b) $2.75$

c) $3.8$

d) $3.375$

e) $1.05$

f) $2.3125$

**Question 16**

Convert the following decimals to fractions. Leave your answers as mixed numbers, simplifying where necessary.

a) $6.15$

b) $1.22$

c) $3.85$

d) $2.84$

e) $9.142$

f) $8.0205$

**Question 17**

Convert the following decimals to fractions. Leave your answers as improper fractions, simplifying where necessary.

a) $3.45$

b) $1.88$

c) $5.505$

d) $10.032$

e) $5.132$

f) $2.8424$

**Question 18**

Convert the following decimals to simplified fractions

a) $0.\dot{3}$

b) $0.\dot{6}$

c) $0.\dot{1}$

d) $0.\dot{2}$

e) $0.\dot{5}$

f) $0.\dot{8}$

g) $0.1\dot{6}$

h) $0.8\dot{3}$

i) $0.\dot{0}\dot{9}$

j) $0.\dot{1}\dot{8}$

k) $0.\dot{4}\dot{5}$

l) $0.\dot{9}\dot{0}$

**Question 19**

Answer the following:

a) Convert $0.\dot{9}$ to a fraction. Explain your answer.

__Answers__

**Question 1**

a) $\frac{1}{10}$

b) $\frac{3}{10}$

c) $\frac{7}{10}$

d) $\frac{9}{10}$

**Question 2**

a) $\frac12$

b) $\frac15$

c) $\frac25$

d) $\frac35$

**Question 3**

a) $\frac{13}{100}$

b) $\frac{23}{100}$

c) $\frac{99}{100}$

d) $\frac{1}{100}$

e) $\frac{9}{100}$

f) $\frac{33}{100}$

**Question 4**

a) $\frac14$

b) $\frac{1}{50}$

c) $\frac{1}{20}$

d) $\frac{1}{25}$

**Question 5**

a) $\frac34$

b) $\frac{3}{20}$

c) $\frac{7}{20}$

d) $\frac{11}{20}$

e) $\frac{3}{50}$

f) $\frac{2}{25}$

**Question 6**

a) $\frac{17}{50}$

b) $\frac{9}{20}$

c) $\frac{27}{50}$

d) $\frac{19}{25}$

e) $\frac{31}{50}$

f) $\frac{22}{25}$

**Question 7**

a) $\frac{123}{1000}$

b) $\frac{533}{1000}$

c) $\frac{3}{1000}$

d) $\frac{63}{1000}$

**Question 8**

a) $\frac{1}{500}$

b) $\frac{1}{200}$

c) $\frac{1}{125}$

d) $\frac{3}{500}$

e) $\frac{2}{500}$

**Question 9**

a) $\frac{61}{500}$

b) $\frac{293}{500}$

c) $\frac{3}{40}$

d) $\frac{84}{125}$

e) $\frac{91}{200}$

f) $\frac{19}{200}$

**Question 10**

a) $\frac{1733}{10000}$

b) $\frac{8237}{10000}$

c) $\frac{5051}{10000}$

d) $\frac{7}{10000}$

e) $\frac{403}{10000}$

f) $\frac{1823}{10000}$

**Question 11**

a) $\frac{2421}{5000}$

b) $\frac{1643}{2000}$

c) $\frac{527}{2500}$

d) $\frac{6}{625}$

e) $\frac{1}{1250}$

f) $\frac{161}{2000}$

**Question 12**

a) $1\frac12$

b) $3\frac{7}{10}$

c) $2\frac15$

d) $9\frac14$

e) $3\frac18$

f) $8\frac{1}{16}$

**Question 13**

a) $\frac72$

b) $\frac{13}{10}$

c) $\frac{21}{5}$

d) $\frac{33}{4}$

e) $\frac98$

f) $\frac{33}{16}$

**Question 14**

a) $3\frac35$

b) $2\frac45$

c) $4\frac34$

d) $1\frac{1}{25}$

e) $10\frac78$

f) $1\frac{13}{16}$

**Question 15**

a) $\frac75$

b) $\frac{11}{4}$

c) $\frac{19}{5}$

d) $\frac{27}{8}$

e) $\frac{21}{20}$

f) $\frac{37}{16}$

**Question 16**

a) $6\frac{3}{20}$

b) $1\frac{11}{50}$

c) $3\frac{17}{20}$

d) $2\frac{21}{25}$

e) $9\frac{71}{500}$

f) $8\frac{41}{2000}$

**Question 17**

a) $\frac{69}{20}$

b) $\frac{47}{25}$

c) $\frac{1101}{200}$

d) $\frac{1254}{125}$

e) $\frac{1283}{250}$

f) $\frac{3553}{1250}$

**Question 18**

a) $\frac13$

b) $\frac23$

c) $\frac19$

d) $\frac29$

e) $\frac59$

f) $\frac89$

g) $\frac16$

h) $\frac56$

i) $\frac{1}{11}$

j) $\frac{2}{11}$

k) $\frac{5}{11}$

l) $\frac{10}{11}$

**Question 19**

a) If $0.\dot{3}=\frac13$ and $0.\dot{6}=\frac23$

Then $0.\dot{9}=\frac33$

However $\frac33=1$.

You have shown that $0.999999\dots=1$

**Question 1**

Convert the following decimals to fractions

a) $0.1$

b) $0.3$

c) $0.7$

d) $0.9$

**Question 2**

Convert the following decimals to simplified fractions

a) $0.5$

b) $0.2$

c) $0.4$

d) $0.6$

**Question 3**

Convert the following decimals to fractions

a) $0.13$

b) $0.23$

c) $0.99$

d) $0.01$

e) $0.09$

f) $0.33$

**Question 4**

Convert the following decimals to simplified fractions

a) $0.25$

b) $0.02$

c) $0.05$

d) $0.04$

**Question 5**

Convert the following decimals to simplified fractions

a) $0.75$

b) $0.15$

c) $0.35$

d) $0.55$

e) $0.06$

f) $0.08$

**Question 6**

Convert the following decimals to simplified fractions

a) $0.34$

b) $0.45$

c) $0.54$

d) $0.76$

e) $0.62$

f) $0.88$

**Question 7**

Convert the following decimals to fractions

a) $0.123$

b) $0.533$

c) $0.003$

d) $0.063$

**Question 8**

Convert the following decimals to simplified fractions

a) $0.002$

b) $0.005$

c) $0.008$

d) $0.006$

e) $0.004$

**Question 9**

Convert the following decimals to simplified fractions

a) $0.122$

b) $0.586$

c) $0.075$

d) $0.672$

e) $0.455$

f) $0.095$

**Question 10**

Convert the following decimals to fractions

a) $0.1733$

b) $0.8237$

c) $0.5051$

d) $0.0007$

e) $0.0403$

f) $0.1823$

**Question 11**

Convert the following decimals to simplified fractions

a) $0.4842$

b) $0.8215$

c) $0.2108$

d) $0.0096$

e) $0.0008$

f) $0.0905$

**Question 12**

Convert the following decimals to fractions. Leave your answers as mixed numbers

a) $1.5$

b) $3.7$

c) $2.2$

d) $9.25$

e) $3.125$

f) $8.0625$

**Question 13**

Convert the following decimals to fractions. Leave your answers as improper fractions

a) $3.5$

b) $1.3$

c) $4.2$

d) $8.25$

e) $1.125$

f) $2.0625$

**Question 14**

Convert the following decimals to fractions. Leave your answers as mixed numbers, simplifying where necessary.

a) $3.6$

b) $2.8$

c) $4.75$

d) $1.04$

e) $10.875$

f) $1.8125$

**Question 15**

Convert the following decimals to fractions. Leave your answers as improper fractions, simplifying where necessary.

a) $1.4$

b) $2.75$

c) $3.8$

d) $3.375$

e) $1.05$

f) $2.3125$

**Question 16**

Convert the following decimals to fractions. Leave your answers as mixed numbers, simplifying where necessary.

a) $6.15$

b) $1.22$

c) $3.85$

d) $2.84$

e) $9.142$

f) $8.0205$

**Question 17**

Convert the following decimals to fractions. Leave your answers as improper fractions, simplifying where necessary.

a) $3.45$

b) $1.88$

c) $5.505$

d) $10.032$

e) $5.132$

f) $2.8424$

**Question 18**

Convert the following decimals to simplified fractions

a) $0.\dot{3}$

b) $0.\dot{6}$

c) $0.\dot{1}$

d) $0.\dot{2}$

e) $0.\dot{5}$

f) $0.\dot{8}$

g) $0.1\dot{6}$

h) $0.8\dot{3}$

i) $0.\dot{0}\dot{9}$

j) $0.\dot{1}\dot{8}$

k) $0.\dot{4}\dot{5}$

l) $0.\dot{9}\dot{0}$

**Question 19**

Answer the following:

a) Convert $0.\dot{9}$ to a fraction. Explain your answer.

__Answers__

**Question 1**

a) $\frac{1}{10}$

b) $\frac{3}{10}$

c) $\frac{7}{10}$

d) $\frac{9}{10}$

**Question 2**

a) $\frac12$

b) $\frac15$

c) $\frac25$

d) $\frac35$

**Question 3**

a) $\frac{13}{100}$

b) $\frac{23}{100}$

c) $\frac{99}{100}$

d) $\frac{1}{100}$

e) $\frac{9}{100}$

f) $\frac{33}{100}$

**Question 4**

a) $\frac14$

b) $\frac{1}{50}$

c) $\frac{1}{20}$

d) $\frac{1}{25}$

**Question 5**

a) $\frac34$

b) $\frac{3}{20}$

c) $\frac{7}{20}$

d) $\frac{11}{20}$

e) $\frac{3}{50}$

f) $\frac{2}{25}$

**Question 6**

a) $\frac{17}{50}$

b) $\frac{9}{20}$

c) $\frac{27}{50}$

d) $\frac{19}{25}$

e) $\frac{31}{50}$

f) $\frac{22}{25}$

**Question 7**

a) $\frac{123}{1000}$

b) $\frac{533}{1000}$

c) $\frac{3}{1000}$

d) $\frac{63}{1000}$

**Question 8**

a) $\frac{1}{500}$

b) $\frac{1}{200}$

c) $\frac{1}{125}$

d) $\frac{3}{500}$

e) $\frac{2}{500}$

**Question 9**

a) $\frac{61}{500}$

b) $\frac{293}{500}$

c) $\frac{3}{40}$

d) $\frac{84}{125}$

e) $\frac{91}{200}$

f) $\frac{19}{200}$

**Question 10**

a) $\frac{1733}{10000}$

b) $\frac{8237}{10000}$

c) $\frac{5051}{10000}$

d) $\frac{7}{10000}$

e) $\frac{403}{10000}$

f) $\frac{1823}{10000}$

**Question 11**

a) $\frac{2421}{5000}$

b) $\frac{1643}{2000}$

c) $\frac{527}{2500}$

d) $\frac{6}{625}$

e) $\frac{1}{1250}$

f) $\frac{161}{2000}$

**Question 12**

a) $1\frac12$

b) $3\frac{7}{10}$

c) $2\frac15$

d) $9\frac14$

e) $3\frac18$

f) $8\frac{1}{16}$

**Question 13**

a) $\frac72$

b) $\frac{13}{10}$

c) $\frac{21}{5}$

d) $\frac{33}{4}$

e) $\frac98$

f) $\frac{33}{16}$

**Question 14**

a) $3\frac35$

b) $2\frac45$

c) $4\frac34$

d) $1\frac{1}{25}$

e) $10\frac78$

f) $1\frac{13}{16}$

**Question 15**

a) $\frac75$

b) $\frac{11}{4}$

c) $\frac{19}{5}$

d) $\frac{27}{8}$

e) $\frac{21}{20}$

f) $\frac{37}{16}$

**Question 16**

a) $6\frac{3}{20}$

b) $1\frac{11}{50}$

c) $3\frac{17}{20}$

d) $2\frac{21}{25}$

e) $9\frac{71}{500}$

f) $8\frac{41}{2000}$

**Question 17**

a) $\frac{69}{20}$

b) $\frac{47}{25}$

c) $\frac{1101}{200}$

d) $\frac{1254}{125}$

e) $\frac{1283}{250}$

f) $\frac{3553}{1250}$

**Question 18**

a) $\frac13$

b) $\frac23$

c) $\frac19$

d) $\frac29$

e) $\frac59$

f) $\frac89$

g) $\frac16$

h) $\frac56$

i) $\frac{1}{11}$

j) $\frac{2}{11}$

k) $\frac{5}{11}$

l) $\frac{10}{11}$

**Question 19**

a) If $0.\dot{3}=\frac13$ and $0.\dot{6}=\frac23$

Then $0.\dot{9}=\frac33$

However $\frac33=1$.

You have shown that $0.999999\dots=1$

__Solutions__

**Question 1**

a)

b)

c)

d)

**Question 2**

a)

b)

c)

d)

**Question 3**

a)

b)

c)

d)

e)

f)

**Question 4**

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b)

c)

d)

**Question 5**

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b)

c)

d)

e)

f)

**Question 6**

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b)

c)

d)

e)

f)

**Question 7**

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b)

c)

d)

**Question 8**

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b)

c)

d)

e)

**Question 9**

a)

b)

c)

d)

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f)

**Question 10**

a)

b)

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d)

e)

f)

**Question 11**

a)

b)

c)

d)

e)

f)

**Question 12**

a)

b)

c)

d)

e)

f)

**Question 13**

a)

b)

c)

d)

e)

f)

**Question 14**

a)

b)

c)

d)

e)

f)

**Question 15**

a)

b)

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d)

e)

f)

**Question 16**

a)

b)

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d)

e)

f)

**Question 17**

a)

b)

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d)

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f)

**Question 18**

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

k)

l)

**Question 19**

a) If $0.\dot{3}=\frac13$ and $0.\dot{6}=\frac23$

Then $0.\dot{9}=\frac33$

However $\frac33=1$.

You have shown that $0.999999\dots=1$