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Year 5 Maths Decimals

Compare & order decimals

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Theory

To compare decimals, line up the decimal points and compare digits place by place from the left. The first place where the digits differ decides. \(0.9\) is bigger than \(0.86\) because \(9\) tenths beats \(8\) tenths, even though \(0.86\) has more digits. This Year 5 maths page shows how to compare, order and place decimals on a number line.

Line up the decimal points so that each place sits under the same place. Compare the ones, then the tenths, then the hundredths, then the thousandths.

Zeros on the end of a decimal do not change its value: \(0.36 = 0.360\). Adding them can make decimals easier to compare.

More digits does not mean bigger. \(0.375\) is less than \(0.4\) because it has only \(3\) tenths.

Ascending order means smallest to largest; descending order means largest to smallest. \(>\) means is greater than and \(<\) means is less than.

Comparing 0.9 and 0.86 in a place value chart A place value chart with columns Ones, Tenths and Hundredths holding 0 and 9. The tenths digit 9 is highlighted; its value is 0.9. OnesTenthsHundredths 09 00.9
\(0.9\) has \(9\) tenths.
Place value chart for 0.86 A place value chart with columns Ones, Tenths, Hundredths holding 0, 8 and 6. The tenths digit 8 is highlighted. OnesTenthsHundredths 086 00.80.06
\(0.86\) has only \(8\) tenths, so \(0.86 < 0.9\).
Number line from 0.6 to 0.7 A number line from 0.6 to 0.7 split into ten equal intervals of one hundredth, labelled at 0.6, 0.65 and 0.7. A red arrow points to the fourth tick after 0.6, which is 0.64. 0.60.650.7
Each interval is \(0.01\); the arrow is at \(0.64\).

Compare place by place from the left:

\[ 0.9 > 0.86 \quad (9 \text{ tenths} > 8 \text{ tenths}) \]
0.9>0.86
\[ 0.36 = 0.360 \]
0.36=0.360
\[ 7.025 < 7.205 < 7.25 < 7.52 \]
7.025<7.205<7.25<7.52
Fill with zeros. To compare \(9.8\), \(9.84\) and \(9.408\), write them as \(9.800\), \(9.840\) and \(9.408\). Now compare them like whole numbers of thousandths.
The first difference decides. Once one place is bigger, the later digits do not matter.

How to compare two decimals

  1. Line up the decimal points.
  2. Add zeros on the end so both have the same number of decimal places.
  3. Compare from the left until two digits are different.
  4. The bigger digit belongs to the bigger number.

How to order several decimals

  1. Write them all with the same number of decimal places.
  2. Order them, then write them as they were given.
Example 1 — Which is larger?
Which is larger, \(0.3\) or \(0.29\)?
Solution
\(0.30\)\(>\)\(0.29\)
0.3>0.29

\(0.3\), because \(3\) tenths is more than \(2\) tenths.

Example 2 — Use a symbol
Write \(>\) or \(<\).
(i) \(5.08\) ___ \(5.8\)
(ii) \(0.71\) ___ \(0.709\)
Solution
\(5.08\)\(<\)\(5.80\)
\(0.710\)\(>\)\(0.709\)
5.08<5.8,0.71>0.709

(i) \(5.08 < 5.8\)
(ii) \(0.71 > 0.709\)

Example 3 — Same value
Which decimal has the same value as \(0.36\): \(0.036\), \(0.360\) or \(3.6\)?
Solution
\(0.36\)\(=\)\(0.360\)
0.36=0.360

\(0.360\). A zero on the end adds no value.

Example 4 — Ascending order
Write \(7.205\), \(7.25\), \(7.025\) and \(7.52\) in ascending order.
Solution

As thousandths: \(7.205\), \(7.250\), \(7.025\), \(7.520\).

\(7.025\)\(<\)\(7.205 < 7.25 < 7.52\)
7.025<7.205<7.25<7.52

\(7.025,\ 7.205,\ 7.25,\ 7.52\).

Example 5 — Race times
Four swimmers took \(9.84\) s, \(9.408\) s, \(9.48\) s and \(9.8\) s.
(i) Which time is the fastest (smallest)?
(ii) Write the times in descending order.
Solution

As thousandths: \(9.840\), \(9.408\), \(9.480\), \(9.800\).

\(9.84\)\(>\)\(9.8 > 9.48 > 9.408\)
9.84>9.8>9.48>9.408

(i) \(9.408\) s
(ii) \(9.84,\ 9.8,\ 9.48,\ 9.408\)

Example 6 — Between
Write a decimal between \(2.6\) and \(2.7\).
Solution
\(2.60\)\(<\)\(2.65 < 2.70\)
2.6<2.65<2.7

\(2.65\) works (so does any decimal from \(2.61\) to \(2.69\)).

Example 7 — Number line
Use the number line diagram. What decimal does the arrow show?
Solution
\(0.6 + 4 \times 0.01\)\(=\)\(0.64\)
0.6+4×0.01=0.64

\(0.64\).

Example 8 — Find the mistake
Liam says \(0.375\) is larger than \(0.4\) because \(375\) is larger than \(4\). Explain why he is wrong.
Solution
\(0.375\)\(<\)\(0.400\)
0.375<0.4

Compare tenths first: \(3\) tenths is less than \(4\) tenths. So \(0.4\) is larger.

Common pitfalls

Longer means larger? No. \(0.375 < 0.4\). Compare place by place, not the number of digits.
Not lining up the points. Compare \(5.08\) and \(5.8\) as \(5.08\) and \(5.80\): the tenths are \(0\) and \(8\).
Thinking end zeros change the value. \(0.36\), \(0.360\) and \(0.3600\) are all equal.
Reading a number line in tenths when it is in hundredths. Work out the size of one interval first.

Frequently asked questions

How do you compare decimals?

Line up the decimal points and compare from the left. The first place that is different decides: \(0.3 > 0.29\).

Is a decimal with more digits bigger?

Not always. \(0.4\) is bigger than \(0.375\) because it has more tenths.

Do zeros at the end of a decimal matter?

No. \(0.36 = 0.360\). They can help you compare.

How do you find a decimal between two decimals?

Add another decimal place: between \(2.6\) and \(2.7\) are \(2.61, 2.62, \ldots, 2.69\).

What is descending order?

Largest to smallest.

More in Decimals
Represent decimals to thousandths
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