We want to find the decimal equivalents for the two given fractions. First, let's take a look at the given fractions.
-4/5 and - 5/6To convert these fractions to a decimal form, we need to divide the numerator of each fraction by its denominator. Let's begin with - 45. Notice that we can divide 4 by 5 without the negative sign and add it to the result.
Notice that the remainder is 0. Because of this, we can say that - 45 written as a decimal is equal to -0.8. Let's do the same for the second fraction. This time, we will divide 5 by 6.
Notice that the products and remainders repeat, so the remainder will never be 0. Because of this, we can say that - 56 written in decimal form is equal to - 0.83.
We want to identify which one of the two decimals is a repeating decimal and which digit is repeating. First, let's recall some important definitions.
Definition
Terminating Decimal
A decimal number whose digits after the decimal point are finite. When written as a fraction and dividing the numerator by the denominator, the remainder is 0.
Repeating Decimal
A decimal number whose some digits after the decimal point repeat infinitely. When written as a fraction and dividing the numerator by the denominator, the products and differences repeat, so the remainder will never be 0.
Keeping this in mind, let's focus on the two decimals we found in Part A.
-0.8 and -0.83
Notice that for - 0.8 there is only one digit after the decimal point, so it is a terminating decimal. For the second decimal number, we can see that there is one digit that repeats infinitely, 3. Because of this, we can say that it is a repeating decimal.
