Question

I cannot find the answer on my own, I need a lil' bit of help.

Consider the number -9/20.
Choose "True" or "False" for each statement.

A. The number is rational.

B. The number can be written as a repeating decimal.

C. Then number is less than -0.4.

I can't do decimals or fractions....I know i'm stupid :/

Answer 1

for any fraction a/b, the decimal format of it is just a ÷ b.

A)

is the number rational?

well, a rational number is one we can write as a ration or fraction, well clearly is a fraction so it is rational.

B)

can it be written as a repeating/recurring decimal? well, 9/20 is 0.45, so -9/20 is -0.45, no repeating decimal like 0.454545......... , just a plain vanilla -0.45, so nope.

C)

is it less than -0.4?

well, let's recall that for the negative side on the number line, the closer to 0, the larger the number, so then -1,000,000 is much smaller than -1, because -1 is closer to 0.

who is closer -0.4 or -0.45?

|--------------------- -0.45 -------- -0.40 ------------------- 0 --------------- 1 -------------------|

so, -0.45 is farther from 0, and therefore is smaller than -0.4, so yes.