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Here you will learn about converting a repeating decimal to a fraction including how to define a repeating decimal.
Students will first learn about converting repeating decimals (often called recurring decimals) to fractions as part of the number system in katex is not definedth grade.
Converting a repeating decimal to fraction is representing the repeating decimals as a fraction without changing its value.
A repeating decimal (recurring decimal) is a decimal number that has a digit (or group of digits) right of the decimal point that repeats forever. The part that repeats can also be shown by placing a line over the first to the last digit of the repeating pattern. Repeating decimals are also known as non-terminating decimals.
For example,
katex is not defined katex is not defined katex is not defined katex is not definedare all repeating decimals.
To convert a repeating decimal to a fraction, you can form an equation. E.g.
katex is not definedKeep track by labeling equations katex is not defined etc.
You need to be able to multiply both sides of this equation confidently by different powers of katex is not defined E.g.
katex is not defined katex is not definedHow does this relate to katex is not definedth grade math?
Use this quiz to check your grade 4 to 6 students’ understanding of converting fractions, decimals and percents. 10+ questions with answers covering a range of 4th, 5th and 6th grade converting fractions, decimals and percents topics to identify areas of strength and support!
DOWNLOAD FREEUse this quiz to check your grade 4 to 6 students’ understanding of converting fractions, decimals and percents. 10+ questions with answers covering a range of 4th, 5th and 6th grade converting fractions, decimals and percents topics to identify areas of strength and support!
DOWNLOAD FREEIn order to convert from a repeating decimal to a fraction, you need to:
Convert katex is not defined to a fraction.
2Multiply both sides of katex is not defined by a power of katex is not defined to create katex is not defined
As katex is not defined has one repeating digit, multiply by katex is not defined Remember, because you are multiplying the whole of katex is not defined by katex is not defined, you also need to multiply the variable katex is not defined by katex is not defined
katex is not defined3Subtract katex is not defined from katex is not defined
Subtract the first equation from the second equation.
katex is not defined4Divide the value by the coefficient of katex is not defined
katex is not definedAs katex is not defined is equal to katex is not defined and katex is not defined it can be stated that katex is not defined and katex is not defined are equal to one another.
5Simplify the fraction.
This fraction cannot be simplified as the only factor that katex is not defined and katex is not defined share is katex is not defined
6State your answer.
katex is not definedConvert katex is not defined to a fraction.
Equate the repeating decimal to a variable, katex is not defined to create katex is not defined
Multiply both sides of katex is not defined by a power of katex is not defined to create katex is not defined
As katex is not defined has two repeating digits, multiply by katex is not defined Remember, because you are multiplying the whole of katex is not defined by katex is not defined you also need to multiply the variable katex is not defined by katex is not defined
katex is not defined
Subtract katex is not defined from katex is not defined
Subtract the first equation from the second equation.
katex is not defined
Divide the value by the coefficient of katex is not defined
Simplify the fraction.
katex is not defined is the greatest common factor of both katex is not defined and katex is not defined so, divide the numerator and the denominator by katex is not defined
katex is not defined
State your answer.
Convert katex is not defined to a fraction.
Equate the repeating decimal to a variable, katex is not defined to create katex is not defined
Multiply both sides of katex is not defined by a power of katex is not defined to create katex is not defined
As katex is not defined has one repeating digit, multiply by katex is not defined Remember, because you are multiplying the whole of katex is not defined by katex is not defined, you also need to multiply the variable katex is not defined by katex is not defined
katex is not defined
Subtract katex is not defined from katex is not defined
Subtract the first equation from the second equation.
katex is not defined
Divide the value by the coefficient of katex is not defined
Simplify the fraction.
Here, notice that there is a decimal as the numerator, so multiply the numerator and the denominator by katex is not defined to remove the decimal.
katex is not defined
You cannot simplify the fraction katex is not defined
State the answer.
Convert katex is not defined to a fraction.
Equate the repeating decimal to a variable, katex is not defined to create katex is not defined
Multiply both sides of katex is not defined by a power of katex is not defined to create katex is not defined
As katex is not defined has two repeating digits, multiply by katex is not defined Remember, because you are multiplying the whole of katex is not defined by katex is not defined, you also need to multiply the variable katex is not defined by katex is not defined
katex is not defined
Subtract katex is not defined from katex is not defined
Subtract the first equation from the second equation.
katex is not defined
Divide the value by the coefficient of katex is not defined
Simplify the fraction.
This fraction cannot be simplified as the only factor that katex is not defined and katex is not defined share is katex is not defined
State the answer.
Convert katex is not defined to a fraction.
Equate the repeating decimal to a variable, katex is not defined to create katex is not defined
Multiply both sides of katex is not defined by a power of katex is not defined to create katex is not defined
As katex is not defined has one repeating digit, you will multiply by katex is not defined Remember, because you are multiplying the whole of katex is not defined by katex is not defined, you also need to multiply the variable katex is not defined by katex is not defined
katex is not defined
Subtract katex is not defined from katex is not defined
Subtract the first equation from the second equation.
katex is not defined
Divide the value by the coefficient of katex is not defined
Simplify the fraction.
This fraction cannot be simplified as the only factor that katex is not defined and katex is not defined share is katex is not defined
State the answer.
Convert katex is not defined to a fraction.
Equate the repeating decimal to a variable, katex is not defined to create katex is not defined
Multiply both sides of katex is not defined by a power of katex is not defined to create katex is not defined
As katex is not defined has two repeating digits, you will multiply by katex is not defined Remember, because you are multiplying the whole of katex is not defined by katex is not defined, you also need to multiply the variable katex is not defined by katex is not defined
katex is not defined
Subtract katex is not defined from katex is not defined
Subtract the first equation from the second equation.
katex is not defined
Divide the value by the coefficient of katex is not defined
Simplify the fraction.
There is a decimal as the numerator, so you will multiply the numerator (and denominator) by katex is not defined
katex is not defined
You can simplify the fraction by dividing the numerator and the denominator by their greatest common factor, katex is not defined
katex is not defined
State the answer.
1. What should you multiply katex is not defined by to help eliminate the repeating decimal?
If the decimal has one repeating digit, then multiply by katex is not defined
katex is not defined
2. What should you multiply katex is not defined by to help eliminate the repeating decimal?
If the decimal has two repeating digits, then multiply by katex is not defined
katex is not defined
3. What should you multiply katex is not defined by to help eliminate the repeating decimal?
If the decimal has two repeating digits, then multiply by katex is not defined
katex is not defined
4. What is katex is not defined as a fraction?
Set the repeating decimal equal to a variable and multiply the sides by the correct multiple of katex is not defined
katex is not defined
Subtract katex is not defined from katex is not defined
katex is not defined
Divide both sides of the equation by katex is not defined
katex is not defined
5. What is katex is not defined as a fraction?
Set the repeating decimal equal to a variable and multiply the sides by the correct multiple of katex is not defined
katex is not defined
Subtract katex is not defined from katex is not defined
katex is not defined
Divide both sides of the equation by katex is not defined.
katex is not defined
This does not simplify further.
6. What is katex is not defined as a fraction?
Set the repeating decimal equal to a variable and multiply the sides by the correct multiple of katex is not defined
katex is not defined
Subtract katex is not defined from katex is not defined
katex is not defined
Divide both sides of the equation by katex is not defined.
katex is not defined
This does not simplify further.
No, both terms can be used synonymously.
A surd is an irrational number expressed in radical form. They cannot be simplified to whole numbers or fractions.
Terminating decimals are decimals that contain a finite number of digits after the decimal point.
Yes. These are called irrational numbers and include pi katex is not defined and Euler’s number katex is not defined
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