Question

write 0.8, 0.0000006, and 0.000000000004 as a fraction, a fraction with a negative exponent, and the product of a single-digit integer and an integer power of ten (10).

Answer 1

0.8 is a decimal number to change it to a fraction make the denominator equal 10 because we have one decimal place

`0.8=(8)/(10)`

we can simplify it by divide up and down by 2

`0.8=(8)/(10)=(4)/(5)`

To write it with a negative exponent we will reciprocal it and make the exponent -1

`0.8=((10)/(8))^(-1)=((5)/(4))^(-1)`

To write it as a product of a single-digit integer and an integer power of ten

Make the denominator 10 = 10^(-1)

`0.8=8*10^(-1)`

Let us do the same with 0.0000006

`0.0000006=(6)/(10000000)`

Because we have 7 decimal places the denominator has 7 zeros

We can divide up and down by 2 to simplify it

`0.0000006=(6)/(10000000)=(3)/(5000000)`

Let us write it with a negative exponent

`0.0000006=((10000000)/(6))^(-1)=((5000000)/(3))^(-1)`

The number as a product of single-digit times 10 to the power is

`0.0000006=6*10^(-7)`

You can do the last number in the same way