Write each decimal as a fraction in lowest terms.

1. 0.111... Answer: 1/9

2. 0.02 Answer: 1/50

3. 0.7272... Answer: 8/11

4. 0.012012... Answer: 4/333 ??

5. 0.66666.... Answer: 2/3

6. 0.396 (reapeating sign over all numbers) Answer: 44/111 ???

If I got any of these wrong, can someone please show me how to do them correctly ?

1. yes

2 yes
3 yes
4 yes
You do not need to do a geometric series to check the answer. Just divide with a calculator.

Oh

5 yes and 6 yes

Hello to everyone

Sure, I can explain how to convert each decimal into a fraction in lowest terms.

1. 0.111...
To convert this repeating decimal to a fraction, we can call it x and subtract it from 10x. By subtracting, we get:
10x - x = 9x, which equals 0.999...
Now, we have the equation 9x = 0.999...
To get rid of the decimal, we move it to the left by multiplying both sides by 10:
90x = 9.999...
Now, subtracting x from both sides, we get:
90x - x = 9.999... - 0.999...
Simplifying further, we have:
89x = 9
Dividing both sides by 89, we get:
x = 9/89
So, 0.111... is equal to 9/89 in lowest terms.

2. 0.02
To convert this decimal to a fraction, we count the number of decimal places, which is 2 in this case. Now, we write the decimal as the numerator and the denominator as 1 followed by as many zeros as there are decimal places:
0.02 = 2/100
Simplifying this fraction gives us 1/50.

3. 0.7272...
Similar to the first question, we can call this decimal x and subtract it from 100x:
100x - x = 72.7272...
Simplifying, we have:
99x = 72.7272...
To remove the repeating decimal, we multiply both sides by 100:
9900x = 7272.7272...
Now, subtracting x from both sides, we have:
9900x - x = 7272.7272... - 72.7272...
Simplifying, we get:
9899x = 7200
Dividing both sides by 9899, we get:
x = 7200/9899
This fraction is already in lowest terms, so 0.7272... is equal to 7200/9899.

4. 0.012012...
Similar to the previous questions, let's call this decimal x and subtract it from 1000x:
1000x - x = 12.012012...
Simplifying, we have:
999x = 12.012012...
To remove the repeating decimal, we multiply both sides by 1000:
999000x = 12012.012012...
Now, subtracting x from both sides, we have:
999000x - x = 12012.012012... - 12.012012...
Simplifying, we get:
998999x = 12000
Dividing both sides by 998999, we get:
x = 12000/998999
This fraction can be simplified to 4/333, so 0.012012... is equal to 4/333 in lowest terms.

5. 0.66666...
Similar to the first question, we can call this decimal x and subtract it from 10x:
10x - x = 6.66666...
Simplifying, we have:
9x = 6.66666...
To remove the repeating decimal, we multiply both sides by 10:
90x = 66.66666...
Now, subtracting x from both sides, we have:
90x - x = 66.66666... - 6.66666...
Simplifying, we get:
89x = 60
Dividing both sides by 89, we get:
x = 60/89
So, 0.66666... is equal to 60/89 in lowest terms.

6. 0.396 (repeating sign over all numbers)
To convert this repeating decimal to a fraction, we can call it x and subtract it from 1000x:
1000x - x = 396.396396...
Simplifying, we have:
999x = 396.396396...
To remove the repeating decimal, we multiply both sides by 1000:
999000x = 396396.396396...
Now, subtracting x from both sides, we have:
999000x - x = 396396.396396... - 396.396396...
Simplifying, we get:
998999x = 396000
Dividing both sides by 998999, we get:
x = 396/999
This fraction can be simplified to 44/111, so 0.396 (repeating) is equal to 44/111 in lowest terms.

I hope this explanation helps! Let me know if you have any more questions.

Thank You!