Comparing and Ordering Decimals
Year 5 · Maths · Free — no account needed
Comparing and Ordering Decimals
A decimal number uses columns after the decimal point. The first column is tenths, the second is hundredths, and the third is thousandths. Each column is ten times smaller than the one before it — just like ones, tens and hundreds, but shrinking instead of growing.
Line up the decimal points
To compare two decimals, line up the decimal points first, then compare digit by digit from left to right: ones, then tenths, then hundredths, then thousandths. The very first column where the digits differ tells you which number is bigger — you can stop comparing after that.
Longer doesn't mean larger
A common trap: 0.125 looks like a "bigger" number than 0.5 because it has more digits. It isn't. Write 0.5 as 0.500 — now compare tenths: 5 tenths beats 1 tenth, so 0.5 is bigger than 0.125. Always compare by place value, never by counting digits.
Numbers greater than one
When numbers have a whole number part, compare that part first. 5.021 is bigger than 4.999, because 5 ones is more than 4 ones — it doesn't matter what comes after the decimal point once the whole numbers are different.
Decimals on a number line
Between any two decimals there are more decimals hiding at the next place value. Between 2.3 and 2.4 there are ten equal steps of one hundredth: 2.31, 2.32, 2.33, and so on. Between 2.30 and 2.31 there are ten equal steps of one thousandth. This means you can always zoom in further to place a decimal exactly.
Worked Example
Order these numbers from smallest to largest: 0.6, 0.58, 0.607 Step 1: Write all three numbers with the same number of decimal places by padding with zeros. 0.6 = 0.600 0.58 = 0.580 0.607 = 0.607 Step 2: Compare the tenths digit first. 0.600 has 6 tenths, 0.580 has 5 tenths, 0.607 has 6 tenths. So 0.580 is the smallest — it can be placed straight away. Step 3: For the remaining two (0.600 and 0.607), the tenths digits match (both 6), so compare hundredths. Both have 0 hundredths, so compare thousandths: 0 versus 7. 0.607 has more thousandths. Step 4: Write the final order, smallest to largest: 0.58, 0.6, 0.607.
Practice
In the number 5.234, what does the digit 3 represent?
Flashcards
What is the value of the third digit after the decimal point?
It is the thousandths digit — each thousandths column is ten times smaller than a hundredths column.
How do you compare two decimals with different numbers of decimal places, like 0.6 and 0.58?
Line up the decimal points, pad the shorter one with zeros (0.60), then compare place by place from left to right.
True or false: a decimal with more digits after the point is always the bigger number?
False — for example 0.5 is bigger than 0.125, because 5 tenths is more than 1 tenth.
When comparing 7.019 and 6.999, what do you compare first?
The whole number part first — 7 is bigger than 6, so 7.019 is bigger, no matter what follows the decimal point.
If a number line between 4.2 and 4.3 is split into 10 equal steps, how big is each step?
One hundredth (0.01) — because tenths are split into ten smaller hundredths.
What is the first step when ordering a list of decimals with different lengths?
Rewrite them all with the same number of decimal places by padding with zeros, so they are easier to compare.
All 15 practice questions
In the number 5.234, what does the digit 3 represent?
- 3 hundredths
- 3 ones
- 3 tenths
- 3 thousandths
Show the answer to question 1
Answer: 3 hundredths
In 5.234, the digits after the decimal point are tenths (2), hundredths (3) and thousandths (4), so the 3 represents 3 hundredths.
In the number 12.809, what is the value of the digit 9?
- 9 thousandths
- 9 tenths
- 9 ones
- 9 hundredths
Show the answer to question 2
Answer: 9 thousandths
In 12.809, tenths = 8, hundredths = 0, thousandths = 9, so the digit 9 represents 9 thousandths.
Which is bigger, 0.6 or 0.58?
- Cannot tell
- 0.58
- 0.6
- They are equal
Show the answer to question 3
Answer: 0.6
Writing 0.6 as 0.60 and comparing tenths digits, 6 tenths is more than 5 tenths, so 0.6 is bigger.
Which is smaller, 3.402 or 3.42?
- 3.42
- Cannot tell
- 3.402
- They are equal
Show the answer to question 4
Answer: 3.402
Writing 3.42 as 3.420, the hundredths digit of 3.402 is 0 while 3.420 has 2, so 3.402 is smaller.
Which of these statements is true?
- 0.5 is smaller because it has fewer digits
- 0.5 is bigger than 0.125 because 5 tenths is more than 1 tenth
- 0.125 is bigger than 0.5 because it has more digits
- 0.125 and 0.5 are equal
Show the answer to question 5
Answer: 0.5 is bigger than 0.125 because 5 tenths is more than 1 tenth
Writing 0.5 as 0.500 and comparing tenths digits, 5 beats 1, so 0.5 is bigger than 0.125 because 5 tenths is more than 1 tenth.
Which is greater, 7.019 or 6.999?
- 7.019
- They are equal
- 6.999
- Cannot tell
Show the answer to question 6
Answer: 7.019
Comparing whole numbers first, 7 is more than 6, so 7.019 is greater.
Order these numbers from smallest to largest: 4.05, 4.5, 4.055
- 4.055, 4.05, 4.5
- 4.05, 4.055, 4.5
- 4.5, 4.055, 4.05
- 4.05, 4.5, 4.055
Show the answer to question 7
Answer: 4.05, 4.055, 4.5
Writing them with equal decimal places gives 4.050, 4.055 and 4.500, so from smallest to largest they are 4.05, 4.055, 4.5.
Order these numbers from largest to smallest: 0.7, 0.699, 0.71
- 0.71, 0.699, 0.7
- 0.7, 0.71, 0.699
- 0.699, 0.7, 0.71
- 0.71, 0.7, 0.699
Show the answer to question 8
Answer: 0.71, 0.7, 0.699
Writing them with equal decimal places gives 0.710, 0.700 and 0.699, so from largest to smallest they are 0.71, 0.7, 0.699.
When comparing 2.456 and 2.465, which place value column should decide the answer?
- the ones digit
- the hundredths digit
- the thousandths digit
- the tenths digit
Show the answer to question 9
Answer: the hundredths digit
The ones (2) and tenths (4) match in both numbers, so compare the hundredths digit: 5 versus 6, the hundredths digit decides it.
A number line from 3.6 to 3.7 is split into 10 equal steps. Which decimal sits at the 4th mark after 3.6?
- 3.64
- 3.4
- 3.604
- 3.46
Show the answer to question 10
Answer: 3.64
Each step is 0.01, so 4 steps from 3.6 gives 3.6 + 0.04 = 3.64.
A number line shows a point exactly halfway between 5.2 and 5.3. Which decimal is at that point?
- 5.25
- 5.35
- 5.2
- 5.15
Show the answer to question 11
Answer: 5.25
Halfway between 5.2 and 5.3 is 5.2 + 0.05 = 5.25.
Point P sits somewhere between 6.7 and 6.8 on a number line, closer to 6.8 than to 6.7. Which decimal could be point P?
- 6.78
- 6.85
- 6.72
- 6.65
Show the answer to question 12
Answer: 6.78
6.78 is only 0.02 away from 6.8 but 0.08 away from 6.7, so it is closer to 6.8, unlike 6.65 or 6.85 which lie outside the 6.7 to 6.8 range.
Which of these numbers has the greatest value: 0.9, 0.09, 0.909, 0.099?
- 0.9
- 0.909
- 0.099
- 0.09
Show the answer to question 13
Answer: 0.909
Writing them with equal decimal places gives 0.900, 0.090, 0.909 and 0.099, so the greatest is 0.909.
Order these numbers from smallest to largest: 3.8, 3.75, 3.805
- 3.805, 3.75, 3.8
- 3.8, 3.75, 3.805
- 3.75, 3.8, 3.805
- 3.75, 3.805, 3.8
Show the answer to question 14
Answer: 3.75, 3.8, 3.805
Writing them with equal decimal places gives 3.750, 3.800 and 3.805, so from smallest to largest they are 3.75, 3.8, 3.805.
What is the value of the digit 4 in 0.462?
- 4 thousandths
- 4 hundredths
- 4 tenths
- 4 ones
Show the answer to question 15
Answer: 4 tenths
In 0.462, the first digit after the decimal point is tenths, so 4 represents 4 tenths.
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