Exercise 26 Page 82

Practice makes perfect

We want to determine whether the given fraction has repeating or terminating decimals. Let's recall some facts about the decimals.

Repeating Decimal Numbers	Terminating Decimal Numbers
A decimal in which some digits after the decimal point repeat infinitely. The digits repeat their values at regular intervals and the infinitely repeated part is not zero.	A decimal with a finite number of digits. Terminating numbers can be written as fractions, which means that they are rational numbers.

Next, let's go over some examples of repeating and terminating decimals.

Repeating Decimal Numbers			Terminating Decimal Numbers
Number	Notation	Fraction	Number	Fraction
0.666666...	0.6	2/3	0.5	1/2
1.454545...	1.45	16/11	1.53	153/100

This table helps us write the given fraction as a decimal number. Recall that 2 15 means 2÷ 15. Therefore, we will divide the numerator by the denominator. Let's do it!

Notice that the pattern starts to repeat itself after a few steps. This means that the decimal is a repeating decimal. We can write it using bar notation. Remember, the bar goes over the decimal part that repeats itself. 0.133333... = 0.13 We found that 215 written as a decimal is 0.13. In this case, the digits in our decimal repeat infinitely. This means that our fraction has repeating decimals.

We want to determine whether the given fraction has repeating or terminating decimals. First, let's write the given fraction as a decimal number. To do so, recall that 11 20 means 11÷ 20. Therefore, we will divide the numerator by the denominator. Let's do it!

We found that 1120 written as a decimal is 0.55. In this case, our decimal has a finite number of digits. This means that our fraction has terminating decimals.

We want to determine whether the given fraction has repeating or terminating decimals. First, let's write the given fraction as a decimal number. To do so, recall that 17 40 means 17÷ 40. Therefore, we will divide the numerator by the denominator. Let's do it!

We found that 1740 written as a decimal is 0.425. In this case, our decimal has a finite number of digits. This means that our fraction has terminating decimals.

We want to determine whether the given fraction has repeating or terminating decimals. First, let's write the given fraction as a decimal number. To do so, recall that 1 12 means 1÷ 12. Therefore, we will divide the numerator by the denominator. Let's do it!

We can see that the pattern starts to repeat itself after a few steps. This means that the decimal is a repeating decimal. We can write it using bar notation. Remember, the bar goes over the decimal part that repeats itself. 0.083333... = 0.083 We found that 112 written as a decimal is 0.083. In this case, the digits in our decimal repeat infinitely. This means that our fraction has repeating decimals.

Subchapter links

2.1.1 Fraction-to-Decimal Conversions p.74-76

2.1.2 Rewriting Decimals as Fractions p.82-83

Exercise 26 Page 82

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