Q1: What fraction is equivalent to the decimal 0.5? (a) \(\frac{1}{2}\) (b) \(\frac{5}{100}\) (c) \(\frac{1}{5}\) (d) \(\frac{5}{10}\)
Solution:
Ans: (a) Explanation: The decimal 0.5 means 5 tenths, which can be written as \(\frac{5}{10}\). When we simplify \(\frac{5}{10}\) by dividing both the numerator and denominator by 5, we get \(\frac{1}{2}\). Both \(\frac{5}{10}\) and \(\frac{1}{2}\) are correct, but \(\frac{1}{2}\) is in simplest form.
Q2: Which decimal represents the fraction \(\frac{3}{10}\)? (a) 0.03 (b) 0.3 (c) 3.0 (d) 0.13
Solution:
Ans: (b) Explanation: The fraction \(\frac{3}{10}\) means 3 parts out of 10, which is written as 0.3 in decimal form. The 3 is in the tenths place. Option (a) 0.03 would be \(\frac{3}{100}\), not \(\frac{3}{10}\).
Q3: What is 0.25 written as a fraction in simplest form? (a) \(\frac{25}{10}\) (b) \(\frac{1}{4}\) (c) \(\frac{2}{5}\) (d) \(\frac{25}{100}\)
Solution:
Ans: (b) Explanation: The decimal 0.25 means 25 hundredths, which is \(\frac{25}{100}\). To simplify, we divide both the numerator and denominator by their greatest common factor, which is 25: \(\frac{25 ÷ 25}{100 ÷ 25} = \frac{1}{4}\).
Q4: Which fraction is the same as 0.7? (a) \(\frac{7}{100}\) (b) \(\frac{7}{10}\) (c) \(\frac{1}{7}\) (d) \(\frac{70}{10}\)
Solution:
Ans: (b) Explanation: The decimal 0.7 has one digit after the decimal point, so it represents 7 tenths, which is written as \(\frac{7}{10}\). Option (a) would be 0.07, and option (d) simplifies to 7, not 0.7.
Q5: What is the simplest form of the fraction that represents 0.50? (a) \(\frac{50}{100}\) (b) \(\frac{5}{10}\) (c) \(\frac{1}{2}\) (d) \(\frac{1}{50}\)
Solution:
Ans: (c) Explanation: The decimal 0.50 is the same as 0.5, which means 50 hundredths or \(\frac{50}{100}\). To find the simplest form, we divide both numerator and denominator by 50: \(\frac{50 ÷ 50}{100 ÷ 50} = \frac{1}{2}\).
Ans: (c) Explanation: The fraction \(\frac{75}{100}\) means 75 parts out of 100, which is 75 hundredths. This is written as 0.75 in decimal form. The 7 is in the tenths place and the 5 is in the hundredths place.
Q7: What fraction represents the decimal 0.09? (a) \(\frac{9}{10}\) (b) \(\frac{9}{100}\) (c) \(\frac{90}{100}\) (d) \(\frac{1}{9}\)
Solution:
Ans: (b) Explanation: The decimal 0.09 has two digits after the decimal point, with 9 in the hundredths place. This means 9 hundredths, which is written as \(\frac{9}{100}\). Option (a) would be 0.9, not 0.09.
Q8: What is 0.4 written as a fraction in simplest form? (a) \(\frac{4}{100}\) (b) \(\frac{1}{4}\) (c) \(\frac{2}{5}\) (d) \(\frac{4}{10}\)
Solution:
Ans: (c) Explanation: The decimal 0.4 means 4 tenths, or \(\frac{4}{10}\). To simplify, we divide both the numerator and denominator by their greatest common factor, which is 2: \(\frac{4 ÷ 2}{10 ÷ 2} = \frac{2}{5}\).
Section B: Fill in the Blanks
Q9: The decimal 0.1 can be written as the fraction __________.
Solution:
Ans: \(\frac{1}{10}\) Explanation: The decimal 0.1 has one digit after the decimal point, representing 1 tenth. This is written as the fraction \(\frac{1}{10}\).
Q10: When converting a decimal to a fraction, the number of digits after the decimal point tells you the __________.
Solution:
Ans: denominator Explanation: The number of digits after the decimal point determines the denominator of the fraction. One digit means tenths (denominator 10), two digits means hundredths (denominator 100).
Q11: The fraction \(\frac{60}{100}\) written in simplest form is __________.
Solution:
Ans: \(\frac{3}{5}\) Explanation: To simplify \(\frac{60}{100}\), we divide both the numerator and denominator by their greatest common factor, which is 20: \(\frac{60 ÷ 20}{100 ÷ 20} = \frac{3}{5}\).
Q12: The decimal 0.20 is equivalent to the fraction __________ in simplest form.
Solution:
Ans: \(\frac{1}{5}\) Explanation: The decimal 0.20 is the same as 0.2, which is \(\frac{20}{100}\). Simplifying by dividing both numerator and denominator by 20 gives \(\frac{1}{5}\).
Q13: A decimal with two digits after the decimal point represents a fraction with a denominator of __________.
Solution:
Ans: 100 Explanation: When a decimal has two digits after the decimal point, it represents hundredths, so the denominator is 100.
Q14: The fraction \(\frac{8}{10}\) written as a decimal is __________.
Solution:
Ans: 0.8 Explanation: The fraction \(\frac{8}{10}\) means 8 tenths, which is written as 0.8 in decimal form.
Section C: Word Problems
Q15: Sarah ran 0.75 of a mile during gym class. What fraction of a mile did she run? Write your answer in simplest form.
Solution:
Ans: Step 1: Convert 0.75 to a fraction: \(0.75 = \frac{75}{100}\) Step 2: Simplify by dividing both numerator and denominator by 25: \(\frac{75 ÷ 25}{100 ÷ 25} = \frac{3}{4}\) Final Answer: \(\frac{3}{4}\) of a mile
Q16: A recipe calls for 0.6 cups of sugar. Write this amount as a fraction in simplest form.
Solution:
Ans: Step 1: Convert 0.6 to a fraction: \(0.6 = \frac{6}{10}\) Step 2: Simplify by dividing both numerator and denominator by 2: \(\frac{6 ÷ 2}{10 ÷ 2} = \frac{3}{5}\) Final Answer: \(\frac{3}{5}\) cups
Q17: Jacob colored 0.35 of his art poster with blue paint. What fraction of his poster did he color blue? Write your answer in simplest form.
Solution:
Ans: Step 1: Convert 0.35 to a fraction: \(0.35 = \frac{35}{100}\) Step 2: Simplify by dividing both numerator and denominator by 5: \(\frac{35 ÷ 5}{100 ÷ 5} = \frac{7}{20}\) Final Answer: \(\frac{7}{20}\) of the poster
Q18: A water bottle is filled with 0.8 liters of water. Write this as a fraction in simplest form.
Solution:
Ans: Step 1: Convert 0.8 to a fraction: \(0.8 = \frac{8}{10}\) Step 2: Simplify by dividing both numerator and denominator by 2: \(\frac{8 ÷ 2}{10 ÷ 2} = \frac{4}{5}\) Final Answer: \(\frac{4}{5}\) liters
Q19: Emma spent 0.15 of her allowance on candy. What fraction of her allowance did she spend? Write your answer in simplest form.
Solution:
Ans: Step 1: Convert 0.15 to a fraction: \(0.15 = \frac{15}{100}\) Step 2: Simplify by dividing both numerator and denominator by 5: \(\frac{15 ÷ 5}{100 ÷ 5} = \frac{3}{20}\) Final Answer: \(\frac{3}{20}\) of her allowance
Q20: A bookshelf has 0.45 of its space filled with books. What fraction of the bookshelf is filled? Write your answer in simplest form.
Solution:
Ans: Step 1: Convert 0.45 to a fraction: \(0.45 = \frac{45}{100}\) Step 2: Simplify by dividing both numerator and denominator by 5: \(\frac{45 ÷ 5}{100 ÷ 5} = \frac{9}{20}\) Final Answer: \(\frac{9}{20}\) of the bookshelf
The document Worksheet (with Solutions): Writing Decimals As Fractions is a part of the Grade 4 Course Math Grade 4.
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