Skills Focused: Understanding Repeating Decimals, Converting Repeating Decimals to Fractions, Number Sense, Application of Mathematics in Context, Pattern Recognition, Algebraic Thinking, Precision and Accuracy, Critical Thinking, Expressing Mathematical Solutions
Mastering the skill of converting repeating decimals to fractions is an important skill for grade 8 students as they advance in mathematics. This Convert Between Repeating Decimals and Fractions Worksheets are designed to make this concept approachable, engaging, and practical. With nine downloadable and printable worksheets, each packed with 15 carefully crafted word problems, students can explore real-life scenarios where repeating decimals and fractions intersect.
Time needed: 2 minutes
Learn step-by-step how to convert the repeating decimal 0.666… into the fraction 2/3.
Let the repeating decimal be x. In this case, x = 0.666…
Multiply x by 10 to move the decimal point one place to the right: 10x = 6.666…
Subtract x from 10x to eliminate the repeating part: 10x – x = 6.666… – 0.666… = 6.
Simplify the equation: 9x = 6, so x = 6/9.
Reduce 6/9 to its simplest form by dividing the numerator and denominator by their GCD, which is 3: x = 2/3.
To convert a repeating decimal into a fraction, follow these steps:
Assign the repeating decimal to a variable: Let x represent the repeating decimal. For example, if the decimal is 0.666…, write x = 0.666….
Multiply to shift the repeating part: Multiply x by a power of 10 that matches the length of the repeating block. For 0.666…, the repeating part has one digit, so multiply by 10: 10x = 6.666….
Subtract the original equation: Subtract x = 0.666… from 10x = 6.666… to eliminate the repeating part. This gives: 10x – x = 6.666… – 0.666…, which simplifies to 9x = 6.
Solve for x: Divide both sides by 9: x = 6/9.
Simplify the fraction: Reduce 6/9 to its simplest form by dividing the numerator and denominator by their greatest common divisor (GCD), which is 3. This gives: x = 2/3.
Final Answer: The repeating decimal 0.666… is equal to the fraction 2/3.
To turn a repeating decimal into a fraction, follow these steps:
Assign the repeating decimal to a variable: Let x represent the repeating decimal. For example, if the decimal is 0.777…, write x = 0.777….
Multiply by a power of 10 to shift the repeating digits: Multiply x by 10, 100, or more, depending on how many digits repeat. For 0.777…, multiply by 10 to get 10x = 7.777….
Subtract the original equation from the new one: Subtract x = 0.777… from 10x = 7.777…:
10x – x = 7.777… – 0.777…, which simplifies to 9x = 7.
Solve for x: Divide both sides by 9: x = 7/9.
Final Answer: The repeating decimal 0.777… is equal to the fraction 7/9.
Learning to convert repeating decimals to fractions is crucial because it builds number sense and helps with advanced math topics like algebra, ratios, and probability. Fractions are also easier to use in equations and practical scenarios, like cooking or splitting bills, where exact values matter.
The key is to recognize the repeating pattern and assign it to a variable. Multiply by 10, 100, or 1,000 to align the repeating digits, then subtract and solve. Always simplify the resulting fraction. Practice helps too—try worksheets with word problems that connect decimals and fractions to real-life scenarios.
