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tatuchka [14]
3 years ago
14

Mike and Beth both write the decimal 0.8 (0.88888...)as a fraction. Mike: 45 Beth: 89 Which student wrote the correct fraction?

How do you know that student is correct? Describe a mistake that could have been made by the student who wrote the incorrect fraction. (5 points)
Mathematics
1 answer:
fenix001 [56]3 years ago
3 0

Answer:

see the explanation

Step-by-step explanation:

we have

0.888...

This is a <u>repeating decimal</u> (Is a decimal that has a digit, or a block of digits, that repeat over and over and over again without ever ending)

Convert to fraction number

Let

x=0.888...

10x=8.888...

Subtract 0.888... from 8.888... to remove the decimal

10x-x=8.888...-0.888...

9x=8

Solve for x

x=8/9

therefore

Mike fraction is incorrect

because 4/5=0.8

0.8 is a <u>terminating decimal </u>(It's a decimal with a finite number of digits)

Mike's mistake was considering the number as a terminating decimal instead of a repeating decimal

Beth is correct

because

If you divide 8/9

the result is 0.8888888...

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Answer:

\frac{3}{3} * \frac{2}{3} *\frac{3}{3} =\frac{2}{3} \ in^3

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Step-by-step explanation:

The question is missing the attached figure.

The edge of each cube used to build this rectangular prism is 1/3 inch long. Based on the attached figure.

the volume of the prism = length × height × width

length = 3 * \frac{1}{3} = \frac{3}{3}

height = 3 * \frac{1}{3} = \frac{3}{3}

width = 2 * \frac{1}{3}= \frac{2}{3}

So the volume of the prism = \frac{3}{3} *\frac{3}{3} *\frac{2}{3} =\frac{2}{3} \  in^{3}

∴ The equation that shows the volume of the prism, in cubic inches

= \frac{3}{3} * \frac{2}{3} *\frac{3}{3} =\frac{2}{3} \ in^3

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Step-by-step explanation:

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