Assessment Direction: Write the following fractions as a decimal 1. \frac{1}{4} 2. \frac{3}{5} 3. \frac{3}{8} 4. \frac{5}{8} 5. \frac{33}{11} 6. \frac{7}{50} 7. \frac{17}{25} 8. 2 \frac{21}{32} 9. \frac{67}{13} 10. 5 \frac{19}{125}
The Correct Answer and Explanation is:
Of course. Here are the correct decimal conversions for the fractions in the image, along with a detailed explanation of the process.
Correct Answers:
- 0.25
- 0.8
- 0.375
- 0.625
- 0.54 (with the 54 repeating, e.g., 0.5454…)
- 0.14
- 0.68
- 2.65625
- 5.153846 (with the 153846 repeating)
- 5.152
Explanation
To convert any fraction into its decimal form, the primary method is to divide the numerator, which is the top number, by the denominator, which is the bottom number. This process of division is what the fraction bar fundamentally represents. The resulting decimal can be either terminating, meaning it ends after a certain number of digits, or repeating, meaning a sequence of digits repeats infinitely.
For several problems on this worksheet, such as 1/4 or 7/50, the division results in a terminating decimal. You simply perform the division: 1 divided by 4 equals 0.25. An alternative method for some fractions involves creating an equivalent fraction with a denominator that is a power of ten, like 10, 100, or 1000. For instance, with 4/5 (problem 2), you can multiply both the numerator and denominator by 2 to get 8/10, which is directly written as the decimal 0.8. Similarly, for 17/25 (problem 7), multiplying the top and bottom by 4 gives 68/100, or 0.68. This shortcut is very efficient for denominators that are factors of powers of ten.
When the denominator has prime factors other than 2 or 5, the decimal will be a repeating one. This is the case for 6/11 (problem 5). Dividing 6 by 11 using long division yields 0.545454…, where the digit pair “54” repeats forever. This is typically written with a line over the repeating block of digits.
The assessment also includes mixed numbers and improper fractions. For a mixed number like 2 and 21/32 (problem 8), the whole number (2) remains to the left of the decimal point. You only need to convert the fractional part, 21/32, by dividing 21 by 32 to get 0.65625. Combining these gives the final answer of 2.65625. For an improper fraction like 67/13 (problem 9), you divide the numerator by the denominator directly. This division results in a whole number and a repeating decimal component.
