Math / Numbers & Operations

Question16. 0.5625
17. 0.90625
Convert the following fractions to decimals. Use a line over the repeating sequence.
20. $\frac{11}{9}$
21. $-\frac{4}{9}$
22. $\frac{7}{11}$
23. $\frac{7}{12}$
24. $\frac{8}{15}$

Studdy Solution

STEP 1

What is this asking? We need to convert a bunch of fractions into decimals, and if the decimal representation repeats, we'll show that with a line over the repeating part. Watch out! Don't forget to indicate the repeating part of the decimal if it has one!

STEP 2

1. Convert 11/9 to a decimal.
2. Convert -4/9 to a decimal.
3. Convert 7/11 to a decimal.
4. Convert 7/12 to a decimal.
5. Convert 8/15 to a decimal.

STEP 3

Alright, let's divide $\frac{11}{9}$ to get our decimal!
Remember, fractions are just fancy division problems!
We're asking, "How many times does 9 go into 11?"

STEP 4

$\frac{11}{9} = 11 \div 9 = 1.2222...$ So, 9 goes into 11 once, with a remainder of 2.
Then 9 goes into 20 twice, with a remainder of 2, and so on.
This creates a repeating decimal!

STEP 5

We can write the final result as $1.\overline{2}$ .
That little line over the 2 tells everyone that the 2 repeats forever!

STEP 6

Now, we have $-\frac{4}{9}$ .
It's just like the last one, but negative!
We can divide just like before.

STEP 7

$\frac{4}{9} = 4 \div 9 = 0.4444...$ So, 9 goes into 4 zero times.
Then 9 goes into 40 four times, with a remainder of 4, and so on.
This also creates a repeating decimal!

STEP 8

Since we started with $-\frac{4}{9}$ , our final result is just the negative of what we calculated: $-0.\overline{4}$ .

STEP 9

Time for $\frac{7}{11}$ !
Let's divide 7 by 11.

STEP 10

$\frac{7}{11} = 7 \div 11 = 0.636363...$ 11 goes into 7 zero times.
Then 11 goes into 70 six times, with a remainder of 4.
Then 11 goes into 40 three times, with a remainder of 7.
See the pattern?
It's repeating!

STEP 11

Our final result is $0.\overline{63}$ .
The 63 repeats forever!

STEP 12

Let's tackle $\frac{7}{12}$ . Divide 7 by 12.

STEP 13

$\frac{7}{12} = 7 \div 12 = 0.583333...$ 12 goes into 7 zero times.
Then 12 goes into 70 five times, with a remainder of 10.
Then 12 goes into 100 eight times, with a remainder of 4.
Then 12 goes into 40 three times, with a remainder of 4, and so on.

STEP 14

Our final result is $0.58\overline{3}$ .
Only the 3 repeats!

STEP 15

Last one!
Let's divide $\frac{8}{15}$ .

STEP 16

$\frac{8}{15} = 8 \div 15 = 0.53333...$ 15 goes into 8 zero times.
Then 15 goes into 80 five times, with a remainder of 5.
Then 15 goes into 50 three times, with a remainder of 5, and so on.

STEP 17

Our final result is $0.5\overline{3}$ .

STEP 18

$1.\overline{2}$ , $-0.\overline{4}$ , $0.\overline{63}$ , $0.58\overline{3}$ , $0.5\overline{3}$

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Question16. 0.562517. 0.90625Convert the following fractions to decimals. Use a line over the repeating sequence.20. 119\frac{11}{9}911​21. −49-\frac{4}{9}−94​22. 711\frac{7}{11}117​23. 712\frac{7}{12}127​24. 815\frac{8}{15}158​

Studdy Solution

STEP 1

What is this asking? We need to convert a bunch of fractions into decimals, and if the decimal representation repeats, we'll show that with a line over the repeating part. Watch out! Don't forget to indicate the repeating part of the decimal if it has one!

STEP 2

1. Convert 11/9 to a decimal.2. Convert -4/9 to a decimal.3. Convert 7/11 to a decimal.4. Convert 7/12 to a decimal.5. Convert 8/15 to a decimal.

STEP 3

Alright, let's **divide** 119\frac{11}{9}911​ to get our decimal!Remember, fractions are just fancy division problems!We're asking, "How many times does **9** go into **11**?"

STEP 4

119=11÷9=1.2222...\frac{11}{9} = 11 \div 9 = 1.2222...911​=11÷9=1.2222... So, **9** goes into **11** once, with a remainder of **2**.Then **9** goes into **20** twice, with a remainder of **2**, and so on.This creates a repeating decimal!

STEP 5

We can write the **final result** as 1.2‾1.\overline{2}1.2.That little line over the **2** tells everyone that the **2** repeats forever!

STEP 6

Now, we have −49-\frac{4}{9}−94​.It's just like the last one, but negative!We can **divide** just like before.

STEP 7

49=4÷9=0.4444...\frac{4}{9} = 4 \div 9 = 0.4444...94​=4÷9=0.4444... So, **9** goes into **4** zero times.Then **9** goes into **40** four times, with a remainder of **4**, and so on.This also creates a repeating decimal!

STEP 8

Since we started with −49-\frac{4}{9}−94​, our **final result** is just the negative of what we calculated: −0.4‾-0.\overline{4}−0.4.

STEP 9

Time for 711\frac{7}{11}117​!Let's **divide** **7** by **11**.

STEP 10

711=7÷11=0.636363...\frac{7}{11} = 7 \div 11 = 0.636363...117​=7÷11=0.636363... **11** goes into **7** zero times.Then **11** goes into **70** six times, with a remainder of **4**.Then **11** goes into **40** three times, with a remainder of **7**.See the pattern?It's repeating!

STEP 11

Our **final result** is 0.63‾0.\overline{63}0.63.The **63** repeats forever!

STEP 12

Let's tackle 712\frac{7}{12}127​. **Divide** **7** by **12**.

STEP 13

STEP 14

Our **final result** is 0.583‾0.58\overline{3}0.583.Only the **3** repeats!

STEP 15

Last one!Let's **divide** 815\frac{8}{15}158​.

STEP 16

815=8÷15=0.53333...\frac{8}{15} = 8 \div 15 = 0.53333...158​=8÷15=0.53333... **15** goes into **8** zero times.Then **15** goes into **80** five times, with a remainder of **5**.Then **15** goes into **50** three times, with a remainder of **5**, and so on.

STEP 17

Our **final result** is 0.53‾0.5\overline{3}0.53.

STEP 18

1.2‾1.\overline{2}1.2, −0.4‾-0.\overline{4}−0.4, 0.63‾0.\overline{63}0.63, 0.583‾0.58\overline{3}0.583, 0.53‾0.5\overline{3}0.53

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Question16. 0.5625
17. 0.90625
Convert the following fractions to decimals. Use a line over the repeating sequence.
20. $\frac{11}{9}$
21. $-\frac{4}{9}$
22. $\frac{7}{11}$
23. $\frac{7}{12}$
24. $\frac{8}{15}$

1. Convert 11/9 to a decimal.
2. Convert -4/9 to a decimal.
3. Convert 7/11 to a decimal.
4. Convert 7/12 to a decimal.
5. Convert 8/15 to a decimal.

Alright, let's divide $\frac{11}{9}$ to get our decimal!
Remember, fractions are just fancy division problems!
We're asking, "How many times does 9 go into 11?"

$\frac{11}{9} = 11 \div 9 = 1.2222...$ So, 9 goes into 11 once, with a remainder of 2.
Then 9 goes into 20 twice, with a remainder of 2, and so on.
This creates a repeating decimal!

We can write the final result as $1.\overline{2}$ .
That little line over the 2 tells everyone that the 2 repeats forever!

Now, we have $-\frac{4}{9}$ .
It's just like the last one, but negative!
We can divide just like before.

$\frac{4}{9} = 4 \div 9 = 0.4444...$ So, 9 goes into 4 zero times.
Then 9 goes into 40 four times, with a remainder of 4, and so on.
This also creates a repeating decimal!

Since we started with $-\frac{4}{9}$ , our final result is just the negative of what we calculated: $-0.\overline{4}$ .

Time for $\frac{7}{11}$ !
Let's divide 7 by 11.

$\frac{7}{11} = 7 \div 11 = 0.636363...$ 11 goes into 7 zero times.
Then 11 goes into 70 six times, with a remainder of 4.
Then 11 goes into 40 three times, with a remainder of 7.
See the pattern?
It's repeating!

Our final result is $0.\overline{63}$ .
The 63 repeats forever!

Let's tackle $\frac{7}{12}$ . Divide 7 by 12.

Our final result is $0.58\overline{3}$ .
Only the 3 repeats!

Last one!
Let's divide $\frac{8}{15}$ .

$\frac{8}{15} = 8 \div 15 = 0.53333...$ 15 goes into 8 zero times.
Then 15 goes into 80 five times, with a remainder of 5.
Then 15 goes into 50 three times, with a remainder of 5, and so on.

Our final result is $0.5\overline{3}$ .

$1.\overline{2}$ , $-0.\overline{4}$ , $0.\overline{63}$ , $0.58\overline{3}$ , $0.5\overline{3}$