Basic Mathematics

Comparing and Ordering Decimals

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Comparing and Ordering Decimals
Numbers are compared by their values. Special symbols are used to show the comparison.
The symbol '<' means "less than."
The symbol '>' means "greater than."
8 < 9 is read "Eight is less than nine."
5 > 2 is read "Five is greater than two."
Comparing and Ordering Decimals
When comparing decimals, look at each place value.
Count the decimal places in each number. Add zeros to the end of any numbers so that each number has the same amount of decimal places.
Adding a 0 after the 8 gives each number three digits after the decimal point.
Comparing and Ordering Decimals
Compare the whole numbers to the left of both decimal points.
If the whole numbers are not the same, the smaller decimal has the smaller whole number. There is no need to compare the digits to the right of the decimal points.
Comparing and Ordering Decimals
If the whole numbers are the same, compare the digits to the right of the decimal points. Start in the tenths position.
Continue comparing the digits to the right of the decimal points until you find the first position where the digits are different.
Both numbers have 45 to the left of the decimal point.
Compare the digits to the right of the decimal point. Both numbers have 3 in the tenths position.
Compare the digits in the hundredths position. 7 is less than 8, so 45.374 is less than 45.38.
Comparing and Ordering Decimals
This can be written using the "less than" symbol:
Comparing and Ordering Decimals
Click on the number that belongs in the box.
57.082 < □
57.085
57.008
57.028
57.013
Question 1 of 10
That's correct. The 2 in the thousandths place is less than 5, so 57.082 is less than 57.085.
Compare the hundredths position in each number. 8 is not less than 0, so 57.082 is not less than 57.008. Try again.
Compare the hundredths position in each number. 8 is not less than 2, so 57.082 is not less than 57.028. Try again.
Compare the hundredths position in each number. 8 is not less than 1, so 57.082 is not less than 57.013. Try again.
Find the first position where the digits are different.
Comparing and Ordering Decimals
Click on the number that belongs in the box.
1.35 > □
1.30
1.36
1.54
1.38
Question 2 of 10
That's correct. The 5 in the hundredths place is greater than 0, so 1.35 is greater than 1.30.
Compare the hundredths position in each number. 5 is not greater than 6, so 1.35 is not greater than 1.36. Try again.
Compare the tenths position in each number. 3 is not greater than 5, so 1.35 is not greater than 1.54. Try again.
Compare the hundredths position in each number. 5 is not greater than 8, so 1.35 is not greater than 1.38. Try again.
Find the first position where the digits are different.
Comparing and Ordering Decimals
Click on the number that belongs in the box.
62.27 < □
62.271
62.2
62.26
62.027
Question 3 of 10
That's correct. 62.27 is the same as 62.270. The 0 in the thousandths place is less than 1, so 62.27 is less than 62.271.
62.2 is the same as 62.20. Compare the hundredths position in each number. 7 is not less than 0, so 62.27 is not less than 62.2. Try again.
Compare the hundredths position in each number. 7 is not less than 6, so 62.27 is not less than 62.26. Try again.
Compare the tenths position in each number. 2 is not less than 0, so 62.27 is not less than 62.027. Try again.
Find the first position where the digits are different.
Comparing and Ordering Decimals
Negative numbers have a value less than zero. Numbers to the left on the number line are less than the numbers to the right.
Both numbers have 2 to the left of the decimal point. Compare the digits to the right of the decimal point. 7 is greater than 2, so 2.75 is greater than 2.25.

However, these are negative numbers, which means that −2.75 is to the left of −2.25 on the number line.
Comparing and Ordering Decimals
The number −2.75 is less than −2.25. This can be written using the "less than" symbol.
Comparing and Ordering Decimals
Click on the number that belongs in the box.
−136.044 < □
−136.008
−136.07
−137.004
−136.44
Question 4 of 10
That's correct. −136.044 is to the left of the −136.008, so −135.044 is less than −136.008.
Compare the hundredths position in each number. −136.044 is to the right of −136.07 on the number line, so −136.044 is greater than −136.07. Try again.
Compare the whole numbers. −136.044 is to the right of −137.004 on the number line, so −136.044 is greater than −137.004. Try again.
Compare the tenths position in each number. −136.044 on the number line, so −136.044 is greater than −136.44. Try again.
Find the first position where the digits are different. Numbers to the left on the number lines are less than numbers on the right.
Comparing and Ordering Decimals
Click on the number that belongs in the box.
−89.16 > □
−89.1
−89.09
−89.016
−89.2
Question 5 of 10
−89.1 is the same as −89.10. Compare the hundredths position in each number. −89.16 is to the left of −89.1 on the number line, so −89.16 is less than −89.1. Try again.
Compare the tenths position in each number. −89.09 is to the right of −89.16 on the number line, so −89.09 is greater than −89.16. Try again.
Compare the tenths position in each number. −89.016 is to the right of −89.16 on the number line, so −89.016 is greater than −89.16. Try again.
That's correct. −89.16 is to the right of −89.2 on the number line, so −89.16 is greater than −89.2.
Find the first position where the digits are different. Numbers to the right on the number line are greater than numbers on the left.
Comparing and Ordering Decimals
Compare numbers when ordering them from least to greatest.
Are these numbers in order from least to greatest?
Add zeroes to the end of any numbers so that each number has the same amount of decimal places. Each of the numbers has the same whole number: 4.
Comparing and Ordering Decimals
Next, compare the digits in the corresponding positions to the right of the decimal points. Start with the tenths position. Three of the numbers have a 0 in the tenths position, and the remaining number has a 4 in the tenths position.

4.07, 4.03 and 4.009 are all less than 4.4.
Compare the hundredths position in the remaining numbers. The digits in the hundredths position are 7, 3 and 0. Sequence the numbers from least to greatest based on these digits.
Comparing and Ordering Decimals
These numbers are ordered from least to greatest.
Comparing and Ordering Decimals
Click on the correct answer.
Which group of numbers is arranged in order from least to greatest?
−142.1, −141.44, −141.008, −141.004
−142.1, −141.008, −141.004, −141.44
−141.004, −141.008, −141.44, −142.1
−141.004, −141.008, −141.44, −142.1
Question 6 of 10
That's correct. These numbers are arranged in order from least to greatest.
−141.44 is not greater than −141.004. Since these are negative numbers, −141.004 is to the right of −141.44 on the number line. −141.004 is greater than −141.44. Try again.
−141.44 is not greater than −141.008. Since these are negative numbers, −141.008 is to the right of −141.44 on the number line. −141.008 is greater than −141.44. Try again.
These numbers are arranged in order from greatest to least. The larger the negative number, the small it is in value. Try again.
Numbers to the left on the number line are less than numbers on the right.
Comparing and Ordering Decimals
Click on the correct answer.
Which group of numbers is arranged in order from least to greatest?
58.004, 58.083, 58.085, 58.8
58.8, 58.085, 58.083, 58.004
58.083, 58.085, 58.004, 58.8
58.8, 58.004, 58.083, 58.085
Question 7 of 10
That's correct. These numbers are arranged in order from least to greatest.
These numbers are arranged in order from greatest to least. Try again.
58.004 is not greater than 58.085. Compare the hundredths position. 0 is not greater than 8, so 58.004 is not greater than 58.085. Try again.
58.004 is not greater than 58.8. The number 58.8 is the same as 58.800. Compare the tenths positions. 0 is not greater than 8, so 58.004 is not greater than 58.8. Try again.
When whole numbers are the same, compare digits in corresponding positions to the right of the decimal points.
Comparing and Ordering Decimals
Click on the correct answer.
Which group of numbers is arranged in order from least to greatest?
1.035, 1.3, 1.36, 1.4
1.035, 1.36, 1.4, 1.3
1.4, 1.36, 1.3, 1.035
1.3, 1.035, 1.36, 1.4
Question 8 of 10
That's correct. These numbers are listed in order from least to greatest.
1.3 is not greater than 1.36. The number 1.3 is the same number as 1.30. Compare the hundredths position in both of these numbers. 0 is not greater than 6, so 1.3 is not greater than 1.36. Try again.
These numbers are listed in order from greatest to least. Try again.
1.035 is not greater than 1.3. Compare the tenths position in both of these numbers. 0 is not greater than 3, so 1.035 is not greater than 1.3. Try again.
When whole numbers are the same, compare digits in corresponding positions to the right of the decimal points.
Comparing and Ordering Decimals
Click on the correct answer.
Which group of numbers is arranged in order from least to greatest?
−87.2, −87.1, −87.016, −87.009
−87.009, −87.016, −87.1, −87.2
−87.1, −87.2, −87.016, −87.009
−87.2, −87.1, −87.009, −87.016
Question 9 of 10
That's correct. These numbers are arranged in order from least to greatest.
These numbers are arranged from greatest to least. The larger the negative number, the smaller it is in value. Try again.
−87.2 is not greater than −87.1. Since these numbers are negative, −87.1 is to the right of −87.2 on the number line. Try again.
−87.016 is not greater than −87.009. Since these are negative numbers, −87.016 is to the left of −87.009 on the number line. Try again.
Numbers to the left on the number line are less than numbers on the right.
Comparing and Ordering Decimals
Click on the correct answer.
Which group of numbers is arranged in order from least to greatest?
65.261, 65.26, 65.2, 65.026
65.026, 65.261, 65.2, 65.26
65.2, 65.026, 65.26, 65.261
65.026, 65.2, 65.26, 65.261
Question 10 of 10
These numbers are arranged in order from greatest to least. Try again.
65.2 is not greater than 65.261. The number 65.2 is the same as 65.200. Compare the hundredths positions. 0 is not greater than 6, so 65.2 is not greater than 65.261. Try again.
65.026 is not greater than 65.2. The number 65.2 is the same as 65.200. Compare the tenths positions. 0 is not greater than 2, so 65.026 is not greater than 65.2. Try again.
That's correct. These numbers are arranged in order from least to greatest.
When whole numbers are the same, compare digits in corresponding positions to the right of the decimal points.
Comparing and Ordering Decimals