Lesson: Converting a Repeating Decimal to a Fraction

In this lesson, we will learn how to write a repeating decimal as a fraction.

Sample Question Videos

  • 03:15
  • 03:32
  • 02:24

Worksheet: 25 Questions • 3 Videos

Q1:

Express 0 . 3 7 5 as a common fraction.

Q2:

Express 3 . 7 2 as a common fraction.

Q3:

Express 0 . 4 3 3 as a common fraction.

Q4:

Express 2 6 . 9 as a rational number.

Q5:

Express 0 . 1 3 + 0 . 7 3 2 as a common fraction.

Q6:

Write − 2 . 7 as a mixed number.

Q7:

Ethan’s test scores in chemistry were 69.4, 78, 81.1, 69.1, and 76.4. Determine his average test score, and using the table, determine his grade.

Grade A B C D F
Average Score 90–100 80–89 70–79 60–69 50–59

Q8:

In a given month, the price of a bag of sugar increased by 5 c e n t s in the first week, increased by another 4 c e n t s in each of the next two weeks, and then decreased by 3 c e n t s in the fourth week. Determine the average change in the price of sugar over these 4 weeks.

Q9:

Express 4 . 1 as a common fraction.

Q10:

Express 1 . 4 2 as a common fraction.

Q11:

Express 2 . 8 3 as a common fraction.

Q12:

Express 3 . 6 1 as a common fraction.

Q13:

Express 0 . 1 5 8 as a common fraction.

Q14:

Express 2 . 5 4 8 as a common fraction.

Q15:

Express 0 . 2 2 + 0 . 2 9 4 as a common fraction.

Q16:

Express 0 . 8 4 + 0 . 2 6 7 as a common fraction.

Q17:

Express 0 . 1 6 + 0 . 9 4 6 as a common fraction.

Q18:

Express 0 . 6 3 + 0 . 9 1 6 as a common fraction.

Q19:

Express 0 . 0 2 + 0 . 9 4 8 as a common fraction.

Q20:

Which of the following geometric sequences can be summed up to infinity?

Q21:

What is the minimum number of terms should be taken from the geometric sequence 4 1 , 8 2 , 1 6 4 , … starting from the first term to make the sum greater than 4,456?

Q22:

If possible, find the sum of the series ∞ 2 + 4 5 .

Q23:

Find the geometric sequence and the sum to infinity given the sum of the first three terms equals 42, the first term exceeds the second term by 24, and all terms are positive.

Q24:

The figure shows the steps to producing a curve 𝐶 . It starts as the boundary of the unit square in Figure (a). In Figure (b), we remove a square quarter of the area of the square in (a). In Figure (c), we add a square quarter of the area that we removed in (b). In Figure (d), we remove a square quarter of the area of the square we added in (c). If we continue to do this indefinitely, we will get the curve 𝐶 . We let 𝑅 be the region enclosed by 𝐶 . By summing a suitable infinite series, find the area of region 𝑅 . Give your answer as a fraction.

Q25:

Find the sum of an infinite number of terms of a geometric sequence starting from the third term given the third term is 1 3 7 2 and the sixth term is − 1 3 5 7 6 .
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