QuestionConvert the following fractions to decimals, using a bar for repeating digits: 7. $\frac{2}{3}$ , 8. $\frac{3}{11}$ , 9. $8 \frac{4}{9}$ .

Studdy Solution

STEP 1

Assumptions1. We need to convert the given fractions to decimal form. . If the decimal representation of the fraction is repeating, we will use a bar over the repeating digits.

STEP 2

Let's start with the first fraction $\frac{2}{}$ . To convert this to a decimal, we perform the division operation.
$\frac{2}{} =2 \div$

STEP 3

Perform the division operation.
$\frac{2}{3} =0.666...$

STEP 4

Since the digit6 is repeating, we use a bar over it to represent the repeating decimal.
$\frac{2}{3} =0.\overline{6}$

STEP 5

Next, let's convert the second fraction $\frac{3}{11}$ to a decimal by performing the division operation.
$\frac{3}{11} =3 \div11$

STEP 6

Perform the division operation.
$\frac{3}{11} =0.272727...$

STEP 7

Since the digits27 are repeating, we use a bar over them to represent the repeating decimal.
$\frac{3}{11} =0.\overline{27}$

STEP 8

Finally, let's convert the mixed number $8 \frac{4}{}$ to a decimal. First, we convert the fractional part $\frac{4}{}$ to a decimal by performing the division operation.
$\frac{4}{} =4 \div$

STEP 9

Perform the division operation.
$\frac{4}{9} =.444...$

STEP 10

Since the digit4 is repeating, we use a bar over it to represent the repeating decimal.
$\frac{4}{9} =0.\overline{4}$

STEP 11

Now, add the whole number part8 to the decimal we just found.
$8 \frac{4}{9} =8 +0.\overline{4}$

STEP 12

Perform the addition operation.
$8 \frac{4}{9} =8.4\overline{4}$ So, the decimal equivalents for the given rational numbers are7. $\frac{2}{} =0.\overline{6}$
8. $\frac{}{11} =0.\overline{27}$
9. $8 \frac{4}{9} =8.4\overline{4}$

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QuestionConvert the following fractions to decimals, using a bar for repeating digits: 7. $\frac{2}{3}$ , 8. $\frac{3}{11}$ , 9. $8 \frac{4}{9}$ .

Studdy Solution

STEP 1

Assumptions1. We need to convert the given fractions to decimal form. . If the decimal representation of the fraction is repeating, we will use a bar over the repeating digits.

STEP 2

Let's start with the first fraction $\frac{2}{}$ . To convert this to a decimal, we perform the division operation.
$\frac{2}{} =2 \div$

STEP 3

Perform the division operation.
$\frac{2}{3} =0.666...$

STEP 4

Since the digit6 is repeating, we use a bar over it to represent the repeating decimal.
$\frac{2}{3} =0.\overline{6}$

STEP 5

Next, let's convert the second fraction $\frac{3}{11}$ to a decimal by performing the division operation.
$\frac{3}{11} =3 \div11$

STEP 6

Perform the division operation.
$\frac{3}{11} =0.272727...$

STEP 7

Since the digits27 are repeating, we use a bar over them to represent the repeating decimal.
$\frac{3}{11} =0.\overline{27}$

STEP 8

Finally, let's convert the mixed number $8 \frac{4}{}$ to a decimal. First, we convert the fractional part $\frac{4}{}$ to a decimal by performing the division operation.
$\frac{4}{} =4 \div$

STEP 9

Perform the division operation.
$\frac{4}{9} =.444...$

STEP 10

Since the digit4 is repeating, we use a bar over it to represent the repeating decimal.
$\frac{4}{9} =0.\overline{4}$

STEP 11

Now, add the whole number part8 to the decimal we just found.
$8 \frac{4}{9} =8 +0.\overline{4}$

STEP 12

Perform the addition operation.
$8 \frac{4}{9} =8.4\overline{4}$ So, the decimal equivalents for the given rational numbers are7. $\frac{2}{} =0.\overline{6}$
8. $\frac{}{11} =0.\overline{27}$
9. $8 \frac{4}{9} =8.4\overline{4}$

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QuestionConvert the following fractions to decimals, using a bar for repeating digits: 7. 23\frac{2}{3}32​, 8. 311\frac{3}{11}113​, 9. 8498 \frac{4}{9}894​.

Studdy Solution

STEP 1

Assumptions1. We need to convert the given fractions to decimal form. . If the decimal representation of the fraction is repeating, we will use a bar over the repeating digits.

STEP 2

Let's start with the first fraction 2\frac{2}{}2​. To convert this to a decimal, we perform the division operation.2=2÷\frac{2}{} =2 \div2​=2÷

STEP 3

Perform the division operation.23=0.666...\frac{2}{3} =0.666...32​=0.666...

STEP 4

Since the digit6 is repeating, we use a bar over it to represent the repeating decimal.23=0.6‾\frac{2}{3} =0.\overline{6}32​=0.6

STEP 5

Next, let's convert the second fraction 311\frac{3}{11}113​ to a decimal by performing the division operation.311=3÷11\frac{3}{11} =3 \div11113​=3÷11

STEP 6

Perform the division operation.311=0.272727...\frac{3}{11} =0.272727...113​=0.272727...

STEP 7

Since the digits27 are repeating, we use a bar over them to represent the repeating decimal.311=0.27‾\frac{3}{11} =0.\overline{27}113​=0.27

STEP 8

Finally, let's convert the mixed number 848 \frac{4}{}84​ to a decimal. First, we convert the fractional part 4\frac{4}{}4​ to a decimal by performing the division operation.4=4÷\frac{4}{} =4 \div4​=4÷

STEP 9

Perform the division operation.49=.444...\frac{4}{9} =.444...94​=.444...

STEP 10

Since the digit4 is repeating, we use a bar over it to represent the repeating decimal.49=0.4‾\frac{4}{9} =0.\overline{4}94​=0.4

STEP 11

Now, add the whole number part8 to the decimal we just found.849=8+0.4‾8 \frac{4}{9} =8 +0.\overline{4}894​=8+0.4

STEP 12

Perform the addition operation.849=8.44‾8 \frac{4}{9} =8.4\overline{4}894​=8.44So, the decimal equivalents for the given rational numbers are7. 2=0.6‾\frac{2}{} =0.\overline{6}2​=0.68. 11=0.27‾\frac{}{11} =0.\overline{27}11​=0.279. 849=8.44‾8 \frac{4}{9} =8.4\overline{4}894​=8.44

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QuestionConvert the following fractions to decimals, using a bar for repeating digits: 7. $\frac{2}{3}$ , 8. $\frac{3}{11}$ , 9. $8 \frac{4}{9}$ .

Let's start with the first fraction $\frac{2}{}$ . To convert this to a decimal, we perform the division operation.
$\frac{2}{} =2 \div$

Perform the division operation.
$\frac{2}{3} =0.666...$

Since the digit6 is repeating, we use a bar over it to represent the repeating decimal.
$\frac{2}{3} =0.\overline{6}$

Next, let's convert the second fraction $\frac{3}{11}$ to a decimal by performing the division operation.
$\frac{3}{11} =3 \div11$

Perform the division operation.
$\frac{3}{11} =0.272727...$

Since the digits27 are repeating, we use a bar over them to represent the repeating decimal.
$\frac{3}{11} =0.\overline{27}$

Finally, let's convert the mixed number $8 \frac{4}{}$ to a decimal. First, we convert the fractional part $\frac{4}{}$ to a decimal by performing the division operation.
$\frac{4}{} =4 \div$

Perform the division operation.
$\frac{4}{9} =.444...$

Since the digit4 is repeating, we use a bar over it to represent the repeating decimal.
$\frac{4}{9} =0.\overline{4}$

Now, add the whole number part8 to the decimal we just found.
$8 \frac{4}{9} =8 +0.\overline{4}$

Perform the addition operation.
$8 \frac{4}{9} =8.4\overline{4}$ So, the decimal equivalents for the given rational numbers are7. $\frac{2}{} =0.\overline{6}$
8. $\frac{}{11} =0.\overline{27}$
9. $8 \frac{4}{9} =8.4\overline{4}$