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.
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