 # Exercises on generating fraction and repeating decimal

The period, the part that repeats after the comma, is 3. Thus, the decimal can be written as: .

We can solve it by two methods:

Method 1: fractional

We add the whole part with a fraction, where the numerator will be the period and, in the denominator, a digit 9 for each digit different from the period. In this particular case, the integer part is zero, so the answer is .

Method 2: algebraic

Step 1: we equate the decimal to x, obtaining equation I. Step 2: we multiply both sides of the equation by 10, obtaining equation II. Step 3: we subtract from equation II the equation I. Step 4: We isolate x and find the generating fraction. The period, the part that repeats after the comma, is 4. Thus, the decimal can be written as: .

We can solve it by two methods:

Method 1: fractional

We add the whole part with a fraction, where the numerator will be the period and, in the denominator, a digit 9 for each digit different from the period. Method 2: algebraic

Step 1: we equate the decimal to x, obtaining equation I.

instagram story viewer Step 2: we multiply both sides of the equation by 10, obtaining equation II. Step 3: we subtract from equation II the equation I. Step 4: We isolate x and find the generating fraction. The period, the part that repeats after the comma, is 41. Thus, the decimal can be written as: .

We can solve it by two methods:

Method 1: fractional

We add the whole part with a fraction, where the numerator will be the period and, in the denominator, a digit 9 for each digit different from the period. Method 2: algebraic

Step 1: we equate the decimal to x, obtaining equation I. Step 2: we multiply both sides of the equation by 100, obtaining equation II. (because there are two digits in the decimal). Step 3: we subtract from equation II the equation I. Step 4: We isolate x and find the generating fraction. We can rewrite as: , where 30 is the period. This is a compound decimal.

Step 1: equal to x. step 2: Multiply both sides of the equation by 10, obtaining equation I.

Since the tithe is compound, this will make it simple. step 3: multiply equation I by 100 on both sides of the equality, obtaining equation II. step 3: Subtract equation I from II. step 4: Isolate the x and do the division. We can rewrite as: , where 45 is the period.

Step 1: equal to x. step 2: multiply both sides of the equation by 10, obtaining equation I.

Since the tithe is compound, this will make it simple. step 3: multiply equation I by 100 on both sides of the equality, obtaining equation II. step 3: Subtract equation I from II. step 4: Isolate the x and do the division. Correct answer: a) 2

Doing the division, we find: Note that the decimal can be rewritten as: The period repeats every 6 digits, and the nearest integer multiple of the 50th decimal place will be:

6 x 8 = 48

Thus, the last digit 3 of the period will occupy the 48th decimal place. Therefore, in the next repetition, the first digit 2 will occupy the 50th position.

Correct answer: b) 89

It is necessary to determine the generating fraction and, after, simplify and add numerator and denominator.

We can rewrite as: , where 36 is the period.

Step 1: equal to x. step 2: multiply both sides of the equation by 1000, obtaining equation I.

Since the tithe is compound, this will make it simple. step 3: multiply equation I by 100 on both sides of the equality, obtaining equation II. step 4: Subtract equation I from II. step 5: isolate the x. Once the generating fraction is determined, we must simplify it. Dividing numerator and denominator by 25, by 9, and again by 9. So just add 1 + 88 = 89.

Correct answer: a) 670

It is necessary to determine the generating fraction and, after, simplify and subtract the numerator and denominator.

We can rewrite as: , where 012 is the period.

Step 1: equal to x obtaining equation I. step 2: multiply both sides of the equation by 1000, obtaining equation II. step 3: Subtract equation I from II. step 4: Isolate the x and do the division. Once the generating fraction is determined, we must simplify it. Dividing numerator and denominator by 3. So just subtract 1 003 - 333 = 670.

Teachs.ru

#### Syntactic analysis exercises (with commented template)

Indicate the only sentence in which the subject is indeterminate.feedback explainedThe verb is in...

#### Exercises on the excretory system (with annotated feedback)

Test your knowledge with the 10 questions then on the excretory system.Take advantage of the comm...

#### Exercises on substances and mixtures (with commented template)

Test your knowledge with the 10 questions below about substances and mixtures. Clear your doubts ...

instagram viewer