Q1: Which digit is in the hundredths place in the decimal 4.567? (a) 4 (b) 5 (c) 6 (d) 7
Solution:
Ans: (c) Explanation: In the decimal 4.567, the digit 4 is in the ones place, 5 is in the tenths place, 6 is in the hundredths place, and 7 is in the thousandths place. Therefore, 6 is in the hundredths place.
Q2: Compare the decimals: 0.58 ___ 0.6. Which symbol correctly completes the comparison? (a) > (b) (c) = (d) ≥
Solution:
Ans: (b) Explanation: To compare, we can write both decimals with the same number of decimal places: 0.58 and 0.60. Since 58 hundredths is less than 60 hundredths, 0.58 < 0.6.="" option="" (a)="" is="" incorrect="" because="" 0.58="" is="" not="" greater="" than="" 0.6.="" option="" (c)="" is="" incorrect="" because="" they="" are="" not="" equal.="" option="" (d)="" is="" incorrect="" because="" 0.58="" is="" not="" greater="" than="" or="" equal="" to="">
Q3: What is the value of the digit 9 in the number 12.093? (a) 9 tenths (b) 9 hundredths (c) 9 thousandths (d) 9 ones
Solution:
Ans: (b) Explanation: In 12.093, the digit 9 is in the hundredths place. This means its value is \(\frac{9}{100}\) or 9 hundredths, which equals 0.09. Option (a) is incorrect because the tenths place contains 0. Option (c) is incorrect because the thousandths place contains 3. Option (d) is incorrect because 9 is not in the ones place.
Q4: Arrange these decimals from least to greatest: 2.45, 2.5, 2.405, 2.54 (a) 2.405, 2.45, 2.5, 2.54 (b) 2.45, 2.405, 2.5, 2.54 (c) 2.5, 2.54, 2.45, 2.405 (d) 2.54, 2.5, 2.45, 2.405
Solution:
Ans: (a) Explanation: First, compare the ones place: all have 2. Next, compare the tenths place: all have either 4 or 5. Writing with same decimal places: 2.450, 2.500, 2.405, 2.540. Comparing: 2.405 < 2.450="">< 2.500="">< 2.540.="" therefore,="" the="" correct="" order="" from="" least="" to="" greatest="" is="" 2.405,="" 2.45,="" 2.5,="">
Q5: Which decimal is equivalent to \(\frac{7}{10} + \frac{3}{100}\)? (a) 0.73 (b) 7.3 (c) 0.703 (d) 0.037
Solution:
Ans: (a) Explanation: \(\frac{7}{10}\) equals 0.7 (7 tenths) and \(\frac{3}{100}\) equals 0.03 (3 hundredths). Adding them: 0.7 + 0.03 = 0.73. Option (b) is incorrect as it represents 7 ones and 3 tenths. Option (c) is incorrect as it represents 7 tenths and 3 thousandths. Option (d) is incorrect as it represents 3 hundredths and 7 thousandths.
Q6: Which statement is true about the decimals 3.8 and 3.80? (a) 3.8 > 3.80 (b) 3.8 <> (c) 3.8 = 3.80 (d) Cannot be compared
Solution:
Ans: (c) Explanation: The decimals 3.8 and 3.80 have the same value. Adding zeros to the right of the last digit after the decimal point does not change the value. Both represent 3 ones and 8 tenths, so 3.8 = 3.80. Options (a) and (b) are incorrect because they are equal. Option (d) is incorrect because they can be compared.
Q7: In which number does the digit 2 have the greatest value: 0.254, 5.024, 1.502, or 3.142? (a) 0.254 (b) 5.024 (c) 1.502 (d) 3.142
Solution:
Ans: (a) Explanation: Compare the place value of 2 in each number: In 0.254, the 2 is in the tenths place = 0.2 In 5.024, the 2 is in the hundredths place = 0.02 In 1.502, the 2 is in the thousandths place = 0.002 In 3.142, the 2 is in the thousandths place = 0.002 The greatest value is 0.2, so the digit 2 has the greatest value in 0.254.
Q8: Round 6.387 to the nearest hundredth. (a) 6.3 (b) 6.38 (c) 6.39 (d) 6.4
Solution:
Ans: (c) Explanation: To round to the nearest hundredth, look at the thousandths place (the third digit after the decimal). In 6.387, the thousandths digit is 7. Since 7 ≥ 5, we round up the hundredths place from 8 to 9. Therefore, 6.387 rounded to the nearest hundredth is 6.39. Option (a) rounds to the nearest tenth. Option (b) rounds down incorrectly. Option (d) rounds to the nearest tenth.
## Section B: Fill in the Blanks
Q9: In the decimal 8.926, the digit 2 is in the __________ place.
Solution:
Ans: hundredths Explanation: The first digit after the decimal point is the tenths place, the second digit is the hundredths place, and the third digit is the thousandths place. In 8.926, the digit 2 is the second digit after the decimal point, so it is in the hundredths place.
Q10: The decimal 0.4 is equivalent to the fraction __________.
Solution:
Ans: \(\frac{4}{10}\) or \(\frac{2}{5}\) Explanation: The decimal 0.4 means 4 tenths, which is written as the fraction \(\frac{4}{10}\). This can also be simplified to \(\frac{2}{5}\) by dividing both the numerator and denominator by 2.
Q11: When comparing decimals, if the ones and tenths places are the same, you must compare the __________ place.
Solution:
Ans: hundredths Explanation: When comparing decimals, we start from the left and compare each place value. If the ones and tenths places are equal, we move to the next place value to the right, which is the hundredths place.
Q12: The value of 5 hundredths written as a decimal is __________.
Solution:
Ans: 0.05 Explanation: Hundredths means the second place after the decimal point. Five hundredths is \(\frac{5}{100}\), which equals 0.05 in decimal form.
Q13: When you add a zero to the right end of a decimal, such as changing 2.5 to 2.50, the value of the decimal __________ (increases/decreases/stays the same).
Solution:
Ans: stays the same Explanation: Adding zeros to the right of the last digit after the decimal point does not change the value of the decimal. Both 2.5 and 2.50 represent the same amount: 2 ones and 5 tenths.
Q14: The expanded form of 7.34 using fractions is 7 + __________ + __________.
Solution:
Ans: \(\frac{3}{10}\) + \(\frac{4}{100}\) Explanation: In expanded form, 7.34 = 7 + 0.3 + 0.04. Using fractions, this is written as 7 + \(\frac{3}{10}\) + \(\frac{4}{100}\), where 3 is in the tenths place and 4 is in the hundredths place.
## Section C: Word Problems
Q15: Sarah ran 3.45 kilometers on Monday and 3.5 kilometers on Tuesday. On which day did she run farther, and by how much?
Solution:
Ans: Step 1: Compare 3.45 and 3.5 by writing them with the same number of decimal places: 3.45 and 3.50. Step 2: Since 3.50 > 3.45, Sarah ran farther on Tuesday. Step 3: Find the difference: 3.50 - 3.45 = 0.05 kilometers. Final Answer: Sarah ran farther on Tuesday by 0.05 kilometers (or 5 hundredths of a kilometer).
Q16: A baker used 2.375 cups of flour for cookies and 2.4 cups of flour for muffins. Which recipe used more flour?
Solution:
Ans: Step 1: Compare 2.375 and 2.4 by writing them with the same number of decimal places: 2.375 and 2.400. Step 2: Compare the digits from left to right. The ones place: both have 2. The tenths place: both have 3 and 4, but we need to compare properly: 2.375 has 3 tenths and 2.400 has 4 tenths. Step 3: Since 2.400 > 2.375, the muffin recipe used more flour. Final Answer: The muffin recipe used more flour.
Q17: Three friends measured their plant heights: Lisa's plant is 15.8 cm, Marcus's plant is 15.75 cm, and Jamie's plant is 15.09 cm. Order the plants from shortest to tallest.
Solution:
Ans: Step 1: Write all measurements with the same number of decimal places: 15.80 cm, 15.75 cm, and 15.09 cm. Step 2: Compare the tenths place first: 15.09 has 0 tenths (smallest), then 15.75 and 15.80 both have 7 and 8 tenths respectively. Step 3: Since 15.09 < 15.75="">< 15.80,="" order="" from="" shortest="" to="" tallest="" is="" jamie's,="" marcus's,="" then=""> Final Answer: Jamie's plant (15.09 cm), Marcus's plant (15.75 cm), Lisa's plant (15.8 cm).
Q18: A store sells apples for $1.25 per pound. If the price increases by $0.08, what will be the new price per pound?
Solution:
Ans: Step 1: Original price = $1.25 Step 2: Increase = $0.08 Step 3: Add the increase to the original price: $1.25 + $0.08 Step 4: Align decimal places: 1.25 + 0.08 = 1.33 Final Answer: The new price will be $1.33 per pound.
Q19: Tom's long jump was 4.56 meters. The school record is 4.6 meters. How much farther does Tom need to jump to tie the school record?
Solution:
Ans: Step 1: School record = 4.6 meters = 4.60 meters Step 2: Tom's jump = 4.56 meters Step 3: Find the difference: 4.60 - 4.56 = 0.04 meters Final Answer: Tom needs to jump 0.04 meters (or 4 hundredths of a meter) farther to tie the school record.
Q20: A rainfall gauge measured 2.08 inches of rain in Week 1, 2.8 inches in Week 2, and 2.008 inches in Week 3. What was the total rainfall over the three weeks?
Solution:
Ans: Step 1: Write all measurements with the same number of decimal places: 2.080, 2.800, and 2.008 inches. Step 2: Add the three amounts: 2.080 + 2.800 + 2.008 Step 3: Add column by column: Thousandths: 0 + 0 + 8 = 8 Hundredths: 8 + 0 + 0 = 8 Tenths: 0 + 8 + 0 = 8 Ones: 2 + 2 + 2 = 6 Total = 6.888 inches Final Answer: The total rainfall over the three weeks was 6.888 inches.
The document Worksheet (with Solutions): Comparing Decimal Place Values is a part of the Grade 5 Course Math Grade 5.
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