Converting fractions to recurring decimals
I can divide the numerator of a fraction by its denominator and know that this results in an equivalent recurring decimal.
Converting fractions to recurring decimals
I can divide the numerator of a fraction by its denominator and know that this results in an equivalent recurring decimal.
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Lesson details
Key learning points
- Dividing the numerator by the denominator may result in an equivalent recurring decimal.
- It can be shown that 1/9, 1/11 and 1/36 have equivalent recurring decimals.
- Using a calculator can help investigate fractions which are equivalent to terminating decimals.
- Using a calculator can help investigate fractions which convert to recurring decimals.
Keywords
Recurring decimals - A recurring decimal is one that has an infinite number of digits after the decimal point.
Common misconception
Converting a fraction to a recurring decimal and then rounding the decimal, gives an accurate answer
The use of fractions is more preferred for accuracy than decimals. e.g 1/3 + 1/3 + 1/3 is not 0.3 + 0.3 + 0.3
To help you plan your year 7 maths lesson on: Converting fractions to recurring decimals, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 7 maths lesson on: Converting fractions to recurring decimals, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
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Prior knowledge starter quiz
6 Questions
Q1.Terminating decimals have a number of digits after the decimal point.
Q2.Without using a calculator, work out the decimal value of $$\frac {13}{20}$$.
Q3.Select all the fractions that can be written as terminating decimals.
Q4.Aisha uses her calculator to convert $$0.668$$ to a fraction. She gets an answer of $$\frac {167}{\square}$$. What number should go in the square?
Q5.Match each fraction to its terminating decimal. You can use a calculator for this question.
$$\frac {73}{160}$$ -
$$0.45625$$
$$\frac {57}{125}$$ -
$$0.456$$
$$\frac {63}{140}$$ -
$$0.45$$
$$\frac {2281}{5000}$$ -
$$0.4562$$
$$\frac {34}{85}$$ -
$$0.4$$
Q6.Sam says that $$231 \over 330$$ is not equivalent to a terminating decimal. Without using a calculator, explain whether Sam is correct or not.
Assessment exit quiz
6 Questions
Q1.A decimal with an infinite repeating pattern of digits is called a decimal.
Q2.Match each decimal given using dot notation to its equivalent decimal.
$$0. \dot 1 \dot 2$$ -
$$0.12121212...$$
$$0. 1 2 \dot 3$$ -
$$0.123333333...$$
$$0. \dot{1} 2 \dot {3}$$ -
$$0.123123123...$$
$$0. \dot 1$$ -
$$0.111111111...$$
$$0. 1\dot 2 \dot 3$$ -
$$0.123232323...$$
Q3.Select all the fractions which are equivalent to a recurring decimal.
Q4.Use short division to write $$8\over15$$ as a decimal.
Q5.Jacob uses his calculator to write $$11\over12$$ as a decimal. His calculator display shows the number $$0.9166666667$$. Jacob says, "This shows my fraction terminates." Is Jacob correct? Explain why.
Q6.Izzy writes the recurring decimal $$0.71\dot6$$ as the fraction $$\frac{\square}{60}$$. What number should she write in the square?