Compare Decimals to Hundredths - 4th Grade Math

1. Chen and Amir each ate part of the same-sized sandwich. Chen ate $0.32$ of a sandwich and Amir ate $0.29$ of a sandwich. Who ate more?
   Answer: Chen The correct answer is B, Chen, because $0.32$ is greater than $0.29$ when the two decimals are compared. Choice A is incorrect since the two decimal values are not equal. Choice C is incorrect because the sandwiches are the same size, so the decimal amounts can be compared directly. Choice D reverses the comparison and picks the smaller amount.
2. Compare $0.39$ and $0.93$. Which symbol makes this true: $0.39$ $\underline{\hspace{2em}}$ $0.93$?
   Answer: < Since 0.39 is less than 0.93, the less-than symbol makes the comparison true. The not-equal symbol is technically true but does not specify the actual relationship being tested. The greater-than symbol reverses the correct direction of the comparison. The equal symbol is incorrect since the two decimals have different values.
3. Compare $0.64$ and $0.46$. Which decimal is greater?
   Answer: 0.64 Comparing tenths first: $0.64$ has 6 tenths and $0.46$ has 4 tenths. Since $6 > 4$, $0.64 > 0.46$. Choice B is incorrect because switching the digits changes the value. Choice D is incorrect because rounding each to the nearest tenth gives different values ($0.6$ and $0.5$), so they are not the same.
4. On a number line from 0 to 1, $0.41$ is to the left of $0.49$. What does this mean?
   Answer: $0.41 < 0.49$ On a number line, numbers further to the left are smaller than numbers to the right. Since $0.41$ sits to the left of $0.49$, it must be the smaller value, so $0.41 < 0.49$. Choice A is incorrect because two different positions on the number line cannot represent equal values. Choice B reverses the relationship, treating the leftward number as the larger one. Choice D is incorrect because both decimals are placed on the same number line and can always be compared.
5. Which decimal is greater: $0.63$ or $0.36$?
   Answer: 0.63 is greater than 0.36 Comparing the tenths digits shows 6 tenths is greater than 3 tenths, so 0.63 is greater than 0.36. Choice B reverses the comparison, naming the smaller decimal as the greater one. Choice C is incorrect because the two decimals have different digit values and are not equal. Choice D is incorrect because both decimals are fully specified numbers that can always be compared. Choice A correctly identifies the greater decimal.
6. Lily is comparing the weights of two packages. Package A weighs $0.08$ kilograms and Package B weighs $0.8$ kilograms. She needs to ship the package that weighs less than $0.1$ kilograms. Which package should she choose?
   Answer: Package A Package A is correct because $0.08$ kilograms is less than $0.1$ kilograms. Package B is incorrect because $0.8$ kilograms is greater than $0.1$ kilograms. Either package is incorrect because Package B does not meet the weight requirement. Neither package is incorrect because Package A does meet the requirement.
7. Which decimal is greater: $0.36$ or $0.63$?
   Answer: 0.63 is greater than 0.36 Comparing the tenths digits shows 6 tenths is greater than 3 tenths, so 0.63 is greater than 0.36. Choice A reverses the true relationship between the two decimals. Choice B is incorrect because the two decimals have different digit values and are not equal. Choice D is incorrect because both decimals are fully specified numbers that can always be compared. Choice C correctly identifies the greater decimal.
8. Keisha and Carlos each filled the same-sized cup. Keisha poured in $0.58$ liters and Carlos poured in $0.85$ liters. Who poured in less?
   Answer: Keisha Keisha poured less because $0.58 < 0.85$. They did not pour the same amount because the two decimals are different. Cannot be determined is incorrect because both amounts are given and the cups are the same size. Carlos poured more, not less, since $0.85 > 0.58$.
9. Sofia poured water into two same-sized cups. One cup has $0.56$ liters and the other has $0.65$ liters. Which amount is greater?
   Answer: $0.65$ This question tests 4th grade ability to compare two decimals to hundredths by reasoning about their size, recognizing that comparisons are valid only when decimals refer to the same whole (CCSS.4.NF.7). To compare decimals, use place value reasoning—compare from left to right, starting with the tenths place, then the hundredths place if the tenths are the same. Comparisons are only valid when both decimals refer to the same whole (same-sized objects or same units). Comparing 0.56 and 0.65, we look at the tenths place: 5 vs 6. Since 5 < 6, we know 0.56 < 0.65. Therefore, 0.56 < 0.65. Choice B (0.65) is correct because comparing place values: tenths place shows 5 < 6, so 0.65 liters > 0.56 liters. This demonstrates understanding of place value comparison for decimals. Choice A (0.56) represents choosing the smaller decimal, which happens when students reverse the comparison or confuse which symbol means greater. To help students: The problem states "same-sized cups," so comparison is valid. Step 1: Compare tenths (5 vs 6: 5 < 6 → 0.65 is greater). Visual: 0.65 means 65 hundredths filled, 0.56 means 56 hundredths filled.
10. $0.74$ $\underline{\hspace{2em}}$ $0.47$. Choose the correct symbol.
    Answer: > 0.74 is greater than 0.47 because 7 tenths is greater than 4 tenths, so 0.74 > 0.47. Choice A is wrong because the two decimals are not equal. Choice B reverses the correct direction of the comparison. Choice C incorrectly allows for equality, which isn't the case here.
11. Which symbol correctly compares $0.47$ and $0.52$?
    Answer: < Comparing the tenths digits shows 4 tenths is less than 5 tenths, so $0.47$ is less than $0.52$. Choice A reverses the true relationship between the two decimals. Choice C is incorrect because the two decimals have different digit values and are not equal. Choice D is incorrect because $0.47$ is not greater than or equal to $0.52$. Choice B correctly shows that $0.47$ is less than $0.52$.
12. Keisha and Carlos each filled the same-sized cup. Keisha poured in $0.58$ liters and Carlos poured in $0.85$ liters. Who poured in less?
    Answer: Keisha Keisha poured less because 0.58 liters is less than 0.85 liters , comparing the tenths digits, 5 is less than 8. Choice A is incorrect because both amounts are given and can be compared directly. Choice B reverses which person poured less. Choice D is wrong because the two amounts are not equal.
13. Compare the decimals. Which symbol makes this true: $0.60$ $\underline{\hspace{2em}}$ $0.06$?
    Answer: > Since 0.60 has 6 tenths while 0.06 has only 6 hundredths, 0.60 is the larger value, so the greater-than symbol makes the statement true, making Choice B correct. Choice A does not show which value is larger. Choice C reverses the comparison and would make the statement false. Choice D is incorrect because 0.60 and 0.06 represent different amounts.
14. Marcus wrote the inequality $0.3 < 0.25 < 0.35$, but his teacher said it is incorrect. Which shows these three numbers correctly ordered from least to greatest?
    Answer: $0.25 < 0.3 < 0.35$ $0.25 < 0.3 < 0.35$ is correct because $0.25$ is the smallest value and $0.35$ is the largest. $0.35 < 0.25 < 0.3$ is incorrect because it places the largest value first. $0.25 < 0.35 < 0.3$ is incorrect because $0.35$ is actually larger than $0.3$. $0.3 < 0.35 < 0.25$ is incorrect because $0.25$ is placed last even though it is the smallest.
15. Emma compared two decimal numbers and wrote $0.6 > 0.59$. To justify her comparison, she needs to explain her reasoning. Which explanation correctly justifies why $0.6 > 0.59$?
    Answer: When written as $0.60$, we can see that $60 > 59$ in the hundredths place, so $0.6 > 0.59$ Rewriting $0.6$ as $0.60$ lets both numbers be compared in hundredths, and since $60 > 59$, this correctly justifies $0.6 > 0.59$. Choice A relies on counting digits rather than comparing actual place values, which is not a valid justification. Choice C uses rounding to whole numbers, which throws away the very information needed to compare these close decimals. Choice D incorrectly shortens $0.59$ to $0.5$, which changes its value instead of preserving it for a fair comparison. Choice B is the only explanation that compares the true values of both decimals correctly.
16. Keisha measured two ribbons with the same ruler. One ribbon is $0.71$ meters long and the other is $0.17$ meters long. Which ribbon is longer?
    Answer: 0.71 meters 0.71 meters is longer than 0.17 meters because in the tenths place, 7 is greater than 1. Choice A reverses the two ribbon lengths. Choices B and C shift the decimal point to a different place value, making the numbers much too large. Always compare digit by digit, starting with the largest place value.
17. Which symbol correctly compares $0.47$ and $0.52$?
    Answer: < Since 0.47 is less than 0.52, the correct symbol is <, making Choice A correct. Choice B, ≤, would only apply if the two decimals could be equal, but they are not. Choice C, =, would mean the two decimals are the same value, which they are not. Choice D, >, would mean 0.47 is greater than 0.52, which is the reverse of the true relationship. Comparing the tenths digit, 4 versus 5, shows right away that 0.47 is the smaller number.
18. Compare $0.81$ and $0.18$. Which symbol makes this true: $0.81\ \underline{\hspace{2em}}\ 0.18$?
    Answer: > 0.81 is greater than 0.18 because 8 tenths is greater than 1 tenth, so 0.81 > 0.18. Choice A is wrong because the two decimals are not equal. Choice B reverses the correct direction of the comparison. Choice C only shows that the numbers differ without stating which one is larger, so it does not complete the comparison the question asks for.
19. Maya has two pieces of ribbon. The first piece is $0.38$ meters long. The second piece is $0.4$ meters long. Which piece of ribbon is longer?
    Answer: The second piece, because $0.4 > 0.38$ Comparing tenths: $0.4$ has 4 tenths, while $0.38$ has only 3 tenths. Since $4 > 3$, $0.4 > 0.38$, so the second piece is longer. Choice A reverses the comparison. Choice C is incorrect because the two lengths are not equal. Choice D compares the digits 38 and 4 directly without lining up the place values, which is not a valid way to compare decimals.
20. Maya and Jamal each measured rope using the same meter stick. Maya has $0.68$ meters and Jamal has $0.63$ meters. Who has more rope?
    Answer: Maya The correct answer is Maya, because 0.68 meters is greater than 0.63 meters when comparing the tenths and hundredths digits. Choice B, Jamal, is incorrect because 0.63 is the smaller decimal amount. Choice C is incorrect because both measurements use the same unit, meters, so there is enough information to compare them. Choice D is incorrect because 0.68 and 0.63 are different values, not equal amounts.

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