Convert decimals to fractions
Converting decimals to fractions is a Grade 7 rational numbers skill in Big Ideas Math, Course 2 (Chapter 2). To convert a terminating decimal, write the digits over a power of 10 matching the decimal places—0.75 becomes 75/100, simplified to 3/4. For repeating decimals, set x equal to the decimal, multiply by a power of 10 to shift the repeating block, subtract the equations, and solve: 0.repeating-3 yields x = 1/3. This algebraic method handles mixed cases like 0.1repeating-6 = 1/6. Mastering both techniques lets students switch fluently between decimal and fraction forms when comparing rational numbers.
Key Concepts
To convert a terminating decimal to a fraction: $0.abc = \frac{abc}{1000}$ (denominator is power of 10 based on decimal places).
To convert a repeating decimal to a fraction: Let $x$ equal the decimal, multiply by appropriate power of 10 to align repeating parts, then subtract and solve for $x$.
Common Questions
How do you convert a terminating decimal like 0.75 to a fraction?
Write the decimal digits (75) over a power of 10 equal to the place value of the last digit (100), giving 75/100. Then simplify by dividing both by 25 to get 3/4.
What is the algebraic method for converting a repeating decimal to a fraction?
Let x equal the repeating decimal. Multiply by the power of 10 that shifts one full repeating block left. Subtract the original equation from the new one to eliminate the repeating part, then solve for x.
How do you convert 0.repeating-3 to a fraction?
Let x = 0.repeating-3. Then 10x = 3.repeating-3. Subtracting gives 9x = 3, so x = 3/9 = 1/3.
How do you handle a decimal like 0.1repeating-6 that has both a non-repeating and repeating part?
Set x = 0.1repeating-6. Multiply by 100 to get 100x = 16.repeating-6 and by 10 to get 10x = 1.repeating-6. Subtract: 90x = 15, so x = 15/90 = 1/6.
Why does the denominator become a power of 10 for terminating decimals?
Each decimal place represents a tenth, hundredth, thousandth, etc. The last digit's place value determines the denominator: one decimal place → 10, two → 100, three → 1000.
How does converting decimals to fractions help with comparing rational numbers?
Having both fraction and decimal forms lets you find common denominators or compare decimal values directly, making ordering rational numbers on a number line more flexible.