Decimal place value and rounding · Primary 4 Mathematics / Primary 5 Foundation Mathematics

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Split the whole into smaller parts

Cut a tenth into ten equal parts. What is each new part called?

The shaded part is one tenth of the whole: 1/10 = 0.1.

Name an equal part

All ten parts have the same size. The stripe marks one of them.

One whole split into ten equal parts. The shaded part is one tenth.

Figure data

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Equal parts in the picture
Whole	Parts in order
One tenth of a whole	marked; empty; empty; empty; empty; empty; empty; empty; empty; empty

Split each tenth into ten equal parts to make hundredths. Split each hundredth into ten equal parts to make thousandths.

Hundredths in one tenth

Thousandths in one hundredth

Show answerHide answer

0.1 = 10/100, and 0.01 = 10/1000. Ten units of one place make one unit of the place immediately to its left. The whole stays the same; only the unit used to count it changes.

Give every digit its place

The cards name the parts of 2.307. The zero holds the hundredths place.

Read the value of each digit

A zero count still has a position. The seven counts thousandths.

The counts of each place-value unit in 2.307.

Figure data

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Values shown on the cards
Set	Values
2.307	2 ones; 3 tenths; 0 hundredths; 7 thousandths

2.307 = 2 + 0.3 + 0.007. In 2.37, the seven counts hundredths instead, so the value changes.

For 2.608, give each place count, including zero.

Whole units

Tenths

Hundredths

Thousandths

Now write the decimal made from 3 whole units, 4 tenths, 0 hundredths and 5 thousandths.

Decimal made from the known parts

In 3.405, why must the zero stay between 4 and 5?

It makes the whole part equal to 30It keeps 5 in the hundredths placeIt keeps 5 in the thousandths place

Show answerHide answer

2.608: 2 whole units, 6 tenths, 0 hundredths and 8 thousandths. The new decimal is 3.405. Writing 3.45 would make the five count hundredths.

One record is wrong. Choose its row and write the correction.

Decimal records

Compare each written decimal with its given place counts.

Given place counts and written decimals

Figure data

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Values shown on the cards
Set	Values
Row A	1 ones; 2 tenths; 0 hundredths; 3 thousandths; 1.203 written
Row B	4 ones; 5 tenths; 0 hundredths; 6 thousandths; 4.056 written

Row to fix

Correct answer

Show the place-value repairHide answer

B needs 4.506. Five tenths belong immediately after the point; the zero keeps the six in thousandths. The written 4.056 instead puts five in hundredths. A is correct: its zero also holds the hundredths place.

Check what the counts name

Look at the decimal. Does each count name the right unit?

One record is wrong. Choose its row and write all four corrected place counts, including zero.

Decimal records

Compare each decimal with its written place counts.

Decimals and written place counts

Figure data

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Values shown on the cards
Set	Values
Row A: 2.704	2 ones; 7 tenths; 0 hundredths; 4 thousandths
Row B: 4.306	4 ones; 0 tenths; 3 hundredths; 6 thousandths

Row to fix

Correct ones

Correct tenths

Correct hundredths

Correct thousandths

Show the place-count repairHide answer

B needs 4 ones, 3 tenths, 0 hundredths and 6 thousandths. Three tenths mean 0.3, not 0.03. The written counts name 4.036 instead of 4.306.

A is correct: 2 ones, 7 tenths, 0 hundredths and 4 thousandths make 2.704.

Which place do you need to compare first?

Compare matching places

Compare 0.6 and 0.58. Write equal place-value units beside each other:

Number	Tenths	Hundredths	Thousandths
0.600	6	0	0
0.580	5	8	0

The first different place decides. Write <, > or =.

0.6 compared with 0.58

Adding zeros at the right end of the fractional part preserves its value. Compare 0.5 and 0.500.

0.5 compared with 0.500

Show answerHide answer

0.6 > 0.58, and 0.5 = 0.500. A longer written decimal is not automatically larger. Putting a zero before the five changes its place: 0.05 means five hundredths.

Compare what remains

Both strips began as one whole. Remove 0.40 from A and 0.65 from B. Compare the amounts left, using <, > or =.

What is left after each removal?

A: remove 0.40: one whole in 20 equal parts. Part 1: removed; Part 2: removed; Part 3: removed; Part 4: removed; Part 5: removed; Part 6: removed; Part 7: removed; Part 8: removed; Part 9: empty; Part 10: empty; Part 11: empty; Part 12: empty; Part 13: empty; Part 14: empty; Part 15: empty; Part 16: empty; Part 17: empty; Part 18: empty; Part 19: empty; Part 20: empty. B: remove 0.65: one whole in 20 equal parts. Part 1: removed; Part 2: removed; Part 3: removed; Part 4: removed; Part 5: removed; Part 6: removed; Part 7: removed; Part 8: removed; Part 9: removed; Part 10: removed; Part 11: removed; Part 12: removed; Part 13: removed; Part 14: empty; Part 15: empty; Part 16: empty; Part 17: empty; Part 18: empty; Part 19: empty; Part 20: empty.

Equal wholes. Crossed parts have been removed; the other parts remain.

Figure data

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Equal parts in the picture
Whole	Parts in order
A: remove 0.40	removed; removed; removed; removed; removed; removed; removed; removed; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty
B: remove 0.65	removed; removed; removed; removed; removed; removed; removed; removed; removed; removed; removed; removed; removed; empty; empty; empty; empty; empty; empty; empty

Equal parts in the picture
Whole	Parts in order
A: remove 0.40	removed; removed; removed; removed; removed; removed; removed; removed; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty
B: remove 0.65	removed; removed; removed; removed; removed; removed; removed; removed; removed; removed; removed; removed; removed; empty; empty; empty; empty; empty; empty; empty

A left compared with B left

Show the two remaining amountsHide answer

A: 1 − 0.40 = 0.60. B: 1 − 0.65 = 0.35. The wholes were equal, so removing the smaller amount leaves the larger remainder. Comparing 0.40 and 0.65 alone would answer a different question.

Find every digit that works

To make 0.3□ < 0.36, the tenths already match. The missing hundredths must be less than 6.

Keep the matching places; change the missing digit

0.3□: 3 tenths; □ hundredths. 0.36: 3 tenths; 6 hundredths.

The tenths match. Changing the missing hundredths changes the comparison.

Figure data

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Values shown on the cards
Set	Values
0.3□	3 tenths; □ hundredths
0.36	3 tenths; 6 hundredths

0, 1, 2, 3, 4 and 5 all work. Six makes the values equal; 7, 8 and 9 make the first value greater. One working digit is only part of the answer.

Write every digit that makes 0.square7 < 0.57 true. Separate the digits with commas.

Every possible digit

Show why the set stops thereHide answer

0.07, 0.17, 0.27, 0.37 and 0.47 are all less than 0.57. Using 5 gives 0.57 = 0.57, which does not work for a strict less-than sign. Using 6, 7, 8 or 9 makes the tenths greater. The complete digit set is 0, 1, 2, 3, 4.

One comparison is wrong. Choose its row and write the correct sign: <, > or =.

Decimal records
Row	Task	Written
A	0.84 compared with 0.804	<
B	0.5 compared with 0.500	=

Row to fix

Correct sign

Show the comparison repairHide answer

A needs >. Write 0.84 as 0.840. Both numbers have eight tenths; four hundredths are greater than zero hundredths.

Compare the first different place

0.84 = 0.840: 0 ones; 8 tenths; 4 hundredths; 0 thousandths. 0.804: 0 ones; 8 tenths; 0 hundredths; 4 thousandths.

Match tenths, then compare hundredths

Figure data

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Values shown on the cards
Set	Values
0.84 = 0.840	0 ones; 8 tenths; 4 hundredths; 0 thousandths
0.804	0 ones; 8 tenths; 0 hundredths; 4 thousandths

B is correct: 0.5 and 0.500 name the same amount.

Make the first decimal greater than the second, even though it has fewer decimal places. Both values must be strictly between 0 and 1. Write the first with 1 decimal place and the second with 2 decimal places.

First decimal (1 decimal place)

Second decimal (2 decimal places)

Show one possible pairHide answer

0.7 > 0.63. Seven tenths are greater than six tenths and three hundredths. The second decimal has more written places but names a smaller amount.

Compare the amounts, not the written lengths

0.7: 7 tenths; 0 hundredths. 0.63: 6 tenths; 3 hundredths.

More decimal places can name a smaller amount

Figure data

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Values shown on the cards
Set	Values
0.7	7 tenths; 0 hundredths
0.63	6 tenths; 3 hundredths

Use 0.7, 0.68 and 0.705. Write every value once in each answer, separated by commas. You may add zeros on the right to compare equal units.

Increasing order, smallest first

Decreasing order, largest first

Which comparison uses equal place values?

0.007, 0.068 and 0.7050.700, 0.680 and 0.7057, 68 and 705

Show answerHide answer

Compare 0.700, 0.680 and 0.705. Increasing order is 0.68 < 0.7 < 0.705. Decreasing order is 0.705 > 0.7 > 0.68.

Seven tenths beat six tenths. Between 0.700 and 0.705, the thousandths decide. Writing 0.7 as 0.700 preserves its value.

One order is wrong. Choose its row and write the correct order, using every value once.

Decimal records
Row	Task	Written
A	Increasing order of 0.6, 0.64, 0.641	0.64, 0.641, 0.6
B	Decreasing order of 0.309, 0.39, 0.3	0.39, 0.309, 0.3

Row to fix

Complete corrected order

Show the order repairHide answer

A needs 0.6, 0.64, 0.641. Compare them as 0.600, 0.640 and 0.641. The hundredths separate the first two; the thousandths separate the last two.

Read the full increasing order

0.6 = 0.600: 6 tenths; 0 hundredths; 0 thousandths. 0.64 = 0.640: 6 tenths; 4 hundredths; 0 thousandths. 0.641: 6 tenths; 4 hundredths; 1 thousandths.

The complete increasing order compares the same units

Figure data

This table is included in print while it is open.

Values shown on the cards
Set	Values
0.6 = 0.600	6 tenths; 0 hundredths; 0 thousandths
0.64 = 0.640	6 tenths; 4 hundredths; 0 thousandths
0.641	6 tenths; 4 hundredths; 1 thousandths

B is correct: its decreasing order is 0.39, 0.309, 0.3.

Find a place for one new value

Keep the first three cards in order

Insert the new card while preserving the order of the three given cards.

Three cards are in increasing order. One new value needs a place.

Figure data

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Values shown on the cards
Set	Values
Already in order	0.36; 0.4; 0.52
New value	0.407

Compare the new value with its possible neighbours. Write all four values in increasing order.

All four decimals, smallest first

Show the neighbouring valuesHide answer

0.400 < 0.407 < 0.520: seven thousandths put the new value above 0.4, while its four tenths keep it below 0.52.

The complete row is 0.36, 0.4, 0.407, 0.52. Writing 0.4 as 0.400 changes no value.

Make your own increasing order

Now choose every value yourself. Keep all three inside the bounds; the bounds themselves are not choices.

Make three different numbers strictly between 0.45 and 0.65, smallest first. Each must be a whole number of hundredths.

First number

Middle number

Last number

Show two possible rowsHide answer

0.48, 0.55, 0.62 works: 45 < 48 < 55 < 62 < 65 hundredths.

0.46, 0.50, 0.64 also works. The middle value can be written as 0.5. Each row uses three different values, all strictly inside the bounds. Using a bound, repeating a value or reversing two neighbours would break a rule.

Can you name this amount as both a fraction and a decimal?

Use tenths or hundredths

3/5 = 6/10 = 0.6.

3/4 = 75/100 = 0.75.

Look at the denominator, the bottom number. Is it a factor of 10 or 100? Then change the fraction into tenths or hundredths. To reverse a decimal, count its smallest written unit: 0.125 = 125/1000 = 1/8.

Write 0.035 as a fraction in simplest form. Then write 7/20 as a decimal. For a fraction, use a slash, such as 3/4.

0.035 as a fraction in simplest form

7/20 as a decimal

Why are 0.035 and 0.35 different?

The same digits, apart from zeros, always mean equal valuesThe extra zero makes 0.035 larger35 thousandths differs from 35 hundredths

Show answerHide answer

0.035 = 35/1000 = 7/200.

7/20 = 35/100 = 0.35. The first is thirty-five thousandths; the second is thirty-five hundredths. Their similar digits name different amounts.

One record is wrong. Choose its row and write the correction.

Decimal records
Row	Task	Written
A	0.084, as a fraction in simplest form	84/1000
B	0.125, as a fraction in simplest form	1/8

Row to fix

Correct fraction in simplest form

Show the fraction-form repairHide answer

A needs 21/250. The decimal is 84 thousandths, so 84/1000 has the right value. It is not in simplest form: divide both counts by four to get 21/250.

Count the unit before simplifying

0.084: 8 hundredths; 4 thousandths. Same amount: 84 thousandths.

Count the decimal in thousandths, then simplify

Figure data

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Values shown on the cards
Set	Values
0.084	8 hundredths; 4 thousandths
Same amount	84 thousandths

B is correct: 0.125 = 125/1000 = 1/8.

One record is wrong. Choose its row and write the correction.

Decimal records
Row	Task	Written
A	3/20, as a decimal	0.15
B	9/25, as a decimal	0.036

Row to fix

Correct decimal

Show the decimal-form repairHide answer

B needs 0.36. Multiply both counts in 9/25 by four: 36/100 means 36 hundredths. The written 0.036 instead means 36 thousandths.

The same amount in hundredths and decimal places

9/25 = 36/100: 36 hundredths. 0.36: 3 tenths; 6 hundredths.

Thirty-six hundredths make 0.36

Figure data

This table is included in print while it is open.

Values shown on the cards
Set	Values
9/25 = 36/100	36 hundredths
0.36	3 tenths; 6 hundredths

A is correct: 3/20 = 15/100 = 0.15.

Which two rounded values is your number between?

Round to the place asked for

For 4.376, compare the neighbouring multiples of the unit shown.

Place to round to	Neighbours	Rounded value
Whole number	4 and 5	4
One decimal place	4.3 and 4.4	4.4
Two decimal places	4.37 and 4.38	4.38

The chosen unit decides which digits stay. At a halfway point, choose the larger one. Keep the original number for later calculations unless a question asks you to use the rounded value.

Round 6.284 to two decimal places. Write both decimal places.

Rounded number

Show answerHide answer

6.28, written to two decimal places. The gap to 6.28 is 0.004; the gap to 6.29 is 0.006.

One record is wrong. Choose its row and write the correction.

Decimal records
Row	Task	Written
A	5.376, rounded to 2 decimal places	5.37
B	4.267, rounded to 2 decimal places	4.27

Row to fix

Correct answer

Show the rounding repairHide answer

A needs 5.38. The gaps from 5.376 are 0.006 to 5.37 and 0.004 to 5.38. The smaller gap decides. B is correct: 4.267 is nearer 4.27 than 4.26.

Round 9.995 in three ways. Use the original number each time.

Nearest whole number

One decimal place

Two decimal places

Why keep the zeros in 10.00 when rounding to two decimal places?

They show the hundredths place asked forThey make the value larger than 10They mean the original was exactly 10

Show answerHide answer

10, 10.0, 10.00. To two decimal places, 9.995 is halfway between 9.99 and 10.00. The carry passes through the hundredths and tenths into the whole-number part. All three answers have the same value. The zeros at the end show the accuracy asked for.

Which starting numbers could round to this value?

Find every possible original digit

Which digits make 2.6□4 round to 2.6, to one decimal place? The halfway point is 2.650. Compare the originals on either side.

The box digit moves the original across halfway

Box digit 4: 2.644 original; 2.6 1 place. Halfway: 2.650 original; 2.7 1 place. Box digit 5: 2.654 original; 2.7 1 place.

The last original below halfway and the first original above it give different reports.

Figure data

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Values shown on the cards
Set	Values
Box digit 4	2.644 original; 2.6 1 place
Halfway	2.650 original; 2.7 1 place
Box digit 5	2.654 original; 2.7 1 place

Digits 0 to 4 give originals from 2.604 to 2.644, all below halfway. Digits 5 to 9 give 2.654 to 2.694, all above it. So the complete set is 0, 1, 2, 3, 4. One working digit would leave the answer incomplete.

Write every digit for the box so that 3.8square6, rounded directly to 1 decimal place, gives 3.9.

Separate the digits with commas.

Every possible digit

Check both edges of the digit setHide answer

5, 6, 7, 8, 9 give originals from 3.856 to 3.896. All lie above 3.850 and below 3.950, so each rounds to 3.9. Digit 4 gives 3.846, below the lower halfway point; every smaller digit is below it too.

Work backwards from a rounded report

A report says 2.3, rounded to one decimal place. Which originals could it hide? Use up to two decimal places.

Keep the first halfway point; stop before the next

On an enlarged number line, 2.25 is included and 2.35 is excluded from the interval rounding to 2.3 at one decimal place. The last allowed hundredth is 2.34.

Include the filled end. Leave out the open end. Starting values have up to two decimal places.

Figure data

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The edges and last allowed hundredth
Position	Value
Included halfway	2.25
Rounded report	2.3
Last hundredth	2.34
Excluded next halfway	2.35

2.25 is halfway between 2.2 and 2.3, so it rounds up to 2.3. 2.35 rounds up to 2.4 instead. With hundredths as our smallest unit, the last allowed number before 2.35 is 2.34.

So the possible originals run from 2.25 to 2.34, including both ends. Using thousandths would change the last possible original: the precision matters.

A number is 4.7 when rounded to 1 decimal place.

Find the smallest and largest possible original numbers from 0 to 9.99, using up to 2 decimal places. At halfway, choose the higher number.

Smallest original number

Largest original number

Show the intervalHide answer

The smallest is 4.65 and the largest is 4.74. The lower halfway point rounds up to 4.7. The next halfway point, 4.75, rounds up to 4.8, so the last hundredth that works is 4.74.

Check the neighbours: 4.64 rounds to 4.6 and 4.75 rounds to 4.8. One value that works does not tell you the full range.

Can rounding twice give a different report?

Keep the original for a new accuracy

Round 4.746 directly to one decimal place: 4.7. Now follow the other path in the picture.

One original, two rounding paths

Direct to 1 place: 4.746 original; 4.7 1 place. First to 2 places: 4.746 original; 4.75 2 places. Then to 1 place: 4.75 2 places; 4.8 1 place.

The same original gives different reports along the two rounding paths.

Figure data

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Values shown on the cards
Set	Values
Direct to 1 place	4.746 original; 4.7 1 place
First to 2 places	4.746 original; 4.75 2 places
Then to 1 place	4.75 2 places; 4.8 1 place

Rounding to two decimal places first gives 4.75. That is halfway between 4.7 and 4.8, so rounding it again gives 4.8. The original 4.746 was below that halfway point. Keep the original whenever you need a different rounding place.

Choose an original that rounds to 2.3 when rounded to 1 decimal place.

Rounding it first to 2 decimal places and then to 1 decimal place must give a different report.

Use up to 3 decimal places, from 0 to 9.999.

One possible original number

Show one original and both checksHide answer

2.346 works. Directly to one decimal place, it gives 2.3. To two decimal places, it gives 2.35, which then rounds to 2.4.

The originals 2.345 to 2.349, in thousandths, all work. 2.344 stays below 2.35 even after rounding to hundredths; 2.350 already rounds directly to 2.4. Check both paths whenever you test another original.

Round both numbers to more and more places. When do they stop looking the same?

When do the reports become different?

0.407 and 0.436 are different originals. Rounding can hide that difference. Read across each row, starting with whole numbers.

Two originals at three accuracies

Originals: 0.407; 0.436. Nearest whole: 0; 0. 1 decimal place: 0.4; 0.4. 2 decimal places: 0.41; 0.44.

The reports first become different at two decimal places.

Figure data

This table is included in print while it is open.

Values shown on the cards
Set	Values
Originals	0.407; 0.436
Nearest whole	0; 0
1 decimal place	0.4; 0.4
2 decimal places	0.41; 0.44

Both whole-number reports are 0. Both tenths reports are 0.4. The hundredths reports, 0.41 and 0.44, are different. So 2 decimal places is the first accuracy here that tells the originals apart.

Round 0.749 and 0.751 directly from the originals.

Choose the fewest decimal places that give different rounded reports: 0 (nearest whole number), 1 or 2. Write the place count and both rounded reports at that accuracy. Keep exactly the chosen number of decimal places.

Fewest decimal places

Rounded report for 0.749

Rounded report for 0.751

Show answerHide answer

Both starting values round to the whole number 1. Their answers at 0 places are the same. At 1 decimal place, the reports are 0.7 and 0.8. That is the first difference.

Directly to hundredths, both give 0.75. Finer reports can coincide near a halfway point even when coarser reports differ. Check each accuracy from the originals; do not round an earlier report again.

Can the same rounded reports hide different orders?

Two reports can allow either order

Only the rounded reports are known: A gives 1.2 to one decimal place, and B gives 1.24 to two places. Look at two possible pairs of originals.

Opposite orders, the same reports

A smaller: 1.232 A; 1.241 B. Rounded reports: 1.2 1 place; 1.24 2 places. A larger: 1.248 A; 1.236 B. Rounded reports: 1.2 1 place; 1.24 2 places.

Opposite original orders give exactly the same two rounded reports.

Figure data

This table is included in print while it is open.

Values shown on the cards
Set	Values
A smaller	1.232 A; 1.241 B
Rounded reports	1.2 1 place; 1.24 2 places
A larger	1.248 A; 1.236 B
Rounded reports	1.2 1 place; 1.24 2 places

The first pair has A smaller than B. The other has A larger than B. Both give the same reports. Those reports alone cannot settle the original order.

Original A is reported as 2.6 to 1 decimal place. Original B is reported as 2.63 to 2 decimal places.

Show that either original could be larger. Give one pair with A smaller than B and another with A larger than B. Each pair must round directly to the reports shown.

Use numbers from 0 to 2.999 with up to 3 decimal places.

A smaller: original A

A smaller: original B

A larger: original A

A larger: original B

Show two pairs and their checksHide answer

A = 2.620, B = 2.630 gives A below B. A = 2.640, B = 2.630 gives A above B.

Both A originals round to 2.6 to one decimal place. Both B originals round to 2.63 to two places. You have shown why these reports allow either original order.

Which number is closer to one?

Which is nearer to 1: 0.98 or 1.03? Find each gap before choosing.

Use one reference for both gaps

A number line from 0.96 to 1.04, with 0.98 below one and 1.03 above one. Each small interval is one hundredth.

Compare how far each number is from one.

Figure data

This table is included in print while it is open.

Positions on the number line
Position	Value
below	0.98
reference	1.00
above	1.03

Gap from 0.98 to 1

Gap from 1 to 1.03

The value nearer to 1

Which comparison decides what is nearer to 1?

Compare gaps 0.02 and 0.03Always choose the value below 1Always choose the value above 1

Show answerHide answer

1 − 0.98 = 0.02, while 1.03 − 1 = 0.03. The smaller gap is 0.02, so 0.98 is nearer. Being above or below one does not by itself decide distance.

For a grown-up

Pip’s synthetic voice uses the University of Edinburgh’s Alba speech dataset, via Piper’s Alba voice, under CC BY 4.0. Audio is optional.

Syllabus and review details

Primary 4 Mathematics 2024 · 2021-updated-2025-10
Primary 5 Foundation Mathematics 2025 · 2021-updated-2025-10

Last reviewed: 2026-11-07

Split the whole into smaller parts

Exchange tenths, hundredths and thousandths

Give every digit its place

Read places, then build a number

Keep the empty place when checking a record

Check what the counts name

Repair all four place counts

Compare matching places

Compare what remains

Compare the amounts left

Find every digit that works

Now the missing digit is in a different place

Keep place value in the comparison

More places, smaller value?

Put the values in order

Every value belongs in the corrected row

Find a place for one new value

Where does the new value belong?

Make your own increasing order

Three different values, one increasing row

Use tenths or hundredths

Write it in the form asked for

Write the fraction in its simplest form

Keep hundredths as hundredths

Round to the place asked for

Keep two decimal places

Check the rounding in both records

Keep the places after a carry

Find every possible original digit

Find the complete set for a new report

Work backwards from a rounded report

Recover both ends of a new report

Keep the original for a new accuracy

Choose a number whose two paths disagree

When do the reports become different?

Choose an accuracy and write both reports

Two reports can allow either order

Make both orders possible for new reports

Which value is nearer?

Questions