Question

HELP PLEASE!! Calculators cannot display repeating decimals. Calculators always round.

Yuri's calculator displays decimals to 5 places. He uses his calculator to find the decimal equivalent for each of the fractions below.

For each number, choose what his calculator will display as the decimal equivalent. Then choose whether or not this is the exact decimal equivalent.

Answer 1

image

Explanation:

Answer 2

a.No

b.No

c.Yes

Explanation:

a.We are given that a fraction number

`(1)/(9)`

We have to find that is exact decimal or not.

Calculator display for
`(1)/(9)=0.11111`

It is not an exact decimal equivalent.

`(1)/(9)=0.11111`

A fraction is an exact decimal when the denominator can be expressed as
`2^n\cdot 5^m`.

9 cannot be expressed as
`2^n\cdot 5^m`

Hence,
`(1)/(9)` is not an exact decimal equivalent.

b.
`(7)/(9)`

Calculator display for
`(7)/(9)=0.77778`

It is not an exact decimal equivalent because the denominator of given fraction is 9 which can not be expressed as
`2^n\cdot 5^m`.

Hence, it is not an exact decimal equivalent.

c.
`(9)/(10)`

Calculator display for
`(9)/(10)=0.9`

10=
`2\cdot 5`

It is an exact decimal equivalent because the denominator 10 can be expressed as
`2\cdot 5`.

Hence, the given decimal is an exact decimal equivalent.