Compare Decimals to Thousandths

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5th Grade Math › Compare Decimals to Thousandths

Questions 1 - 10
1

Two water amounts are $0.905$ L and $0.95$ L. Remember: compare decimals place by place after aligning the tenths, hundredths, and thousandths (so $0.95 = 0.950$). Which decimal is greater?​

$0.905$ is greater.

They are equal because they both have 0 ones.

$0.905$ is greater because it has more digits.

$0.95$ is greater.

Explanation

Decimals are compared by examining their place values, from the leftmost digit to the right. We start from the greatest place value, which is the largest unit like ones or tens, and work our way to smaller places like tenths, hundredths, and thousandths. We compare the digits in each corresponding place value one by one until we find a difference. For example, when comparing 0.905 and 0.950 (rewriting 0.95 as 0.950), the tenths digits are both 9, but in the hundredths place, 0 is less than 5, so 0.905 is less than 0.950. A common misconception is assuming numbers are equal if they share the same ones digit, but differences in decimal places matter. By aligning decimals and comparing place by place, we ensure an accurate understanding of their relative values. This method works because place values represent powers of ten, making the comparison systematic and reliable.

2

Two liquids were measured: $3.018$ L and $3.081$ L. Compare the decimals by aligning place values and comparing digits place by place. Which comparison symbol makes the statement true?

$3.018\ \square\ 3.081$

$=$

$>$

$<$

Cannot be determined because there are zeros.

Explanation

Decimals are compared by examining their place values. Begin the comparison from the leftmost place, which is the greatest place value, such as the ones place. Compare the digits in each place value position moving from left to right until you find a difference. For example, when comparing 3.018 and 3.081, the ones and tenths places are the same, but in the hundredths place, 1 is less than 8, so 3.018 < 3.081. A common misconception is that zeros in decimal places don't affect the comparison, but they do when aligning and comparing digit by digit. Using place value ensures all positions up to thousandths are considered equally. This method allows for precise determination of inequalities in measurements like liquid volumes.

3

Two items cost $\$0.608$ and $\$0.68$. To compare, align place values (write $0.68$ as $0.680$) and compare digits place by place. Which decimal is greater?

$0.608$ is greater because 608 is greater than 68.

$0.68$ is greater because $0.680 > 0.608$ when compared place by place.

$0.608$ is greater because it has more digits after the decimal.

$0.608$ is greater because zeros do not matter, so it is the same as $0.68$.

Explanation

Decimals are compared by examining their place values. Begin the comparison from the leftmost place, which is the greatest place value, such as the ones place. Compare the digits in each place value position moving from left to right until you find a difference. For example, when comparing 0.608 and 0.68 (written as 0.680), the tenths places are the same, but in the hundredths place, 0 is less than 8, so 0.608 < 0.680. A common misconception is that more digits after the decimal indicate a larger value, but place values determine the actual size. Using place value ensures equivalent representations like 0.68 and 0.680 are treated properly. This method provides a foolproof way to compare costs or other decimal amounts.

4

A student measured two plant heights: $2.347$ m and $2.374$ m. Line up the decimals by place value (ones, tenths, hundredths, thousandths) and compare place by place. Which comparison symbol makes the statement true?

$2.347\ \square\ 2.374$

$=$

Cannot be determined without rounding

$<$

$>$

Explanation

Decimals are compared by examining their place values. Begin the comparison from the leftmost place, which is the greatest place value, such as the ones place. Compare the digits in each place value position moving from left to right until you find a difference. For example, when comparing 2.347 and 2.374, the ones and tenths places are the same, but in the hundredths place, 4 is less than 7, so 2.347 < 2.374. A common misconception is to ignore the decimal point and compare the digits as whole numbers, like thinking 347 > 374, but this reverses the actual order. Using place value ensures that each digit's position determines its true weight in the number. This approach guarantees accurate comparisons even when decimals have different numbers of places.

5

Two jump distances were recorded: $0.312$ m and $0.321$ m. Compare the decimals by aligning place values and comparing digits place by place. Which comparison symbol makes the statement true?

$0.312\ \square\ 0.321$

$=$

$<$

$>$

Cannot be determined because both start with 0.

Explanation

Decimals are compared by examining their place values. Begin the comparison from the leftmost place, which is the greatest place value, such as the ones place. Compare the digits in each place value position moving from left to right until you find a difference. For example, when comparing 0.312 and 0.321, the tenths places are the same, but in the hundredths place, 1 is less than 2, so 0.312 < 0.321. A common misconception is that numbers starting with zero are equal if their digits look similar, but place values reveal the differences. Using place value ensures precise alignment and step-by-step checking. This technique assures accurate results for comparisons in contexts like jump distances.

6

In a race, Maya ran $1.206$ km and Jordan ran $1.26$ km. Compare the decimals by aligning place values (write $1.26$ as $1.260$) and comparing digits place by place. Which decimal is greater?

$1.206$ is greater because tenths are larger than ones.

$1.206$ is greater because 206 is greater than 26.

$1.26$ is greater because $1.260 > 1.206$ when compared place by place.

$1.26$ is greater because it has fewer digits after the decimal.

Explanation

Decimals are compared by examining their place values. Begin the comparison from the leftmost place, which is the greatest place value, such as the ones place. Compare the digits in each place value position moving from left to right until you find a difference. For example, when comparing 1.206 and 1.26 (written as 1.260), the ones and tenths places are the same, but in the hundredths place, 0 is less than 6, so 1.206 < 1.260. A common misconception is that more digits after the decimal make a number larger, but actually, the value depends on the place values, not the count of digits. Using place value ensures that equivalent forms like 1.26 and 1.260 are recognized as the same. This method provides a reliable way to determine which decimal is greater regardless of how it's written.

7

Two water amounts are $1.208$ L and $1.28$ L. Align the decimals by place value (write $1.28$ as $1.280$) and compare place by place. Which comparison symbol makes the statement true?

$1.208\ \square\ 1.280$

$>$

$<$

$=$

Cannot be compared because one decimal ends in 0.

Explanation

Decimals are compared by examining their place values. Start the comparison from the leftmost place, which is the greatest place value. Compare the digits in each place value position moving from left to right until you find a difference. For example, aligning 1.208 and 1.280 reveals they match in the ones and tenths but differ in the hundredths (0<8), so 1.208 < 1.280. A common misconception is that trailing zeros change a number's value, but they are equivalent when aligning places. Using place value ensures every position is accounted for, from ones to thousandths, for a fair comparison. This method reliably determines relationships between decimals by emphasizing positional importance.

8

Compare the decimals $0.708$ and $0.78$. To compare, line them up as $0.708$ and $0.780$ and go place by place. Which comparison symbol makes the statement true?

$0.708\ \square\ 0.780$

$0.708 > 0.780$

$0.708 = 0.780$

$0.708 > 0.78$ because it has more digits.

$0.708 < 0.780$

Explanation

Decimals are compared by examining their place values, from the leftmost digit to the right. We start from the greatest place value, which is the largest unit like ones or tens, and work our way to smaller places like tenths, hundredths, and thousandths. We compare the digits in each corresponding place value one by one until we find a difference. For example, when comparing 0.708 and 0.780, the tenths digits are both 7, but in the hundredths place, 0 is less than 8, so 0.708 is less than 0.780. A common misconception is believing more digits make a number larger, but we must add zeros to align places for fair comparison. By aligning decimals and comparing place by place, we ensure an accurate understanding of their relative values. This method works because place values represent powers of ten, making the comparison systematic and reliable.

9

Two prices are $\$1.205$ and $\$1.25$. Align the decimals so $1.25 = 1.250$ and compare place by place. Which decimal is greater?​

$\$1.205$ is greater because 205 is greater than 25.

They are equal because both have 1 in the ones place.

$\$1.25$ is greater.

$\$1.205$ is greater.

Explanation

Decimals are compared by examining their place values, from the leftmost digit to the right. We start from the greatest place value, which is the largest unit like ones or tens, and work our way to smaller places like tenths, hundredths, and thousandths. We compare the digits in each corresponding place value one by one until we find a difference. For example, when comparing 1.205 and 1.250 (rewriting 1.25 as 1.250), the ones digits are both 1, the tenths are both 2, but in the hundredths place, 0 is less than 5, so 1.205 is less than 1.250. A common misconception is thinking a number with more digits like 205 is larger than 25, but place values must be aligned first. By aligning decimals and comparing place by place, we ensure an accurate understanding of their relative values. This method works because place values represent powers of ten, making the comparison systematic and reliable.

10

A science class recorded two temperatures: $19.054^\circ\text{C}$ and $19.045^\circ\text{C}$. Compare the decimals place by place (ones, tenths, hundredths, thousandths). Which decimal is greater?​

$19.045^\circ\text{C}$ is greater because 45 is greater than 54.

They are equal because both have 19 ones.

$19.045^\circ\text{C}$ is greater.

$19.054^\circ\text{C}$ is greater.

Explanation

Decimals are compared by examining their place values, from the leftmost digit to the right. We start from the greatest place value, which is the largest unit like ones or tens, and work our way to smaller places like tenths, hundredths, and thousandths. We compare the digits in each corresponding place value one by one until we find a difference. For example, when comparing 19.054 and 19.045, the tens digits are both 1, the ones are both 9, the tenths are both 0, but in the hundredths place, 5 is greater than 4, so 19.054 is greater than 19.045. A common misconception is assuming equality if the ones places match, but decimal places can differ. By aligning decimals and comparing place by place, we ensure an accurate understanding of their relative values. This method works because place values represent powers of ten, making the comparison systematic and reliable.

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