Write as a fraction or mixed number:

1) 0.85
2) 3.6
3) 0.888...

We read 0.85 as eighty-five hundredths. Expressed as a fraction it's 85/100.

Please tell us what you think the other two numbers are expressed as a fraction or mixed number. We'll be glad to critique your answer.

I don't think its a mixed number becausae 85 is'nt greater than 100

is this connectons academy

Round the fraction or mixed number to the nearest 1/2

6/7 (1 point)
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You are correct. The number 0.85 is not a mixed number because the decimal part is not greater than 1. It can be written as a fraction in simplest form as 17/20.

Let's now consider the other numbers.

2) 3.6 can be read as three and six tenths. To express it as a fraction, we can write it as 36/10. However, this fraction is not in simplest form because both the numerator and denominator share a common factor of 2. So, simplifying the fraction, we have 36/10 = 18/5. Therefore, 3.6 as a fraction in simplest form is 18/5.

3) The number 0.888... is a repeating decimal, where the digit 8 repeats indefinitely. To express it as a fraction, we can use the concept of infinite geometric series. We can let x be equal to 0.888..., then multiply both sides by 10 to move the decimal point: 10x = 8.888...

Next, we subtract x from 10x: 10x - x = 8.888... - 0.888... which simplifies to 9x = 8.

Dividing both sides by 9, we get x = 8/9. Therefore, 0.888... as a fraction is 8/9.

You're correct, 0.85 is not a mixed number because it is less than 1. It can be expressed as a fraction simplifying the decimal value.

To convert 0.85 to a fraction, we place the decimal value over 1 and determine the appropriate power of 10 to eliminate the decimal. In this case, we can multiply both the numerator and denominator by 100 to get rid of the decimal point. This gives us the fraction 85/100.

Now, moving on to the other numbers:

2) 3.6 can be read as three and six tenths. Expressed as a mixed number, it would be written as 3 6/10. However, this fraction can be simplified further. We can divide both the numerator and denominator of 6/10 by their greatest common divisor, which is 2. This simplifies the fraction to 3 3/5.

3) 0.888... indicates that the decimal portion repeats indefinitely. To express this as a fraction, we can assign the repeating part, denoted by the ellipsis (...), to a variable. Let x represent the repeating part. To find the fraction, we set up an equation where x is equal to the original decimal value minus the non-repeating part:

x = 0.888... - 0.8

Simplifying this equation gives:

x = 0.0888...

Now, to eliminate the repeating part, we multiply both sides of the equation by a power of 10 that has the same number of digits as the repeating part. In this case, we multiply by 1000:

1000x = 88.888...

Next, subtract the original equation from the new equation to eliminate the repeating part:

1000x - x = 88.888... - 0.0888...

This yields:

999x = 88.8

Now, we solve for x by dividing both sides of the equation by 999:

x = 88.8 / 999

Simplifying the fraction 88.8/999 gives:

x = 8/9

Therefore, 0.888... is equal to 8/9.