Rounding decimals
Rounding decimals to the nearest whole, tenth and hundredth using a number line and place value
About three to four lessons of 45 to 60 minutes
The price is $3.66, so it is about what?
A drink is marked $3.66. If a friend asks roughly how much it costs, you would not say three dollars and sixty-six cents, you would say about $3.70, or maybe about $4. When a runner clocks 12.47 seconds, the commentator says about 12 and a half. When a plank measures 3.472 metres, the builder rounds it to 3.47 metres to write on the cutting list. Every time, we swap an exact decimal for a nearby friendly one that is quicker to say and easier to use.
Rounding a decimal is the same distance question you already know from whole numbers: which friendly number is it nearer to? The trick is knowing which two friendly numbers a decimal sits between, and finding the midpoint. Today you will round decimals to the nearest whole, the nearest tenth and the nearest hundredth on a number line, then use the digit to the right of the rounding place as the fast version of the same decision.
- $3.66 to the nearest tenthabout $3.70, because 3.66 is past 3.65
- 12.47 seconds to the nearest wholeabout 12 seconds, since 12.47 is before 12.5
- 3.472 metres to the nearest hundredth3.47 m, because 3.472 is before 3.475
- A bill of $19.60 to the nearest dollarabout $20, quick to add in your head
What students will be able to do
Students will round decimals to the nearest whole number, tenth and hundredth by locating the decimal between two friendly numbers on a number line, marking the midpoint and deciding which friendly number is nearer, and will use the digit immediately to the right of the rounding place as an equivalent digit rule, handling cases where rounding carries over.
- I can name the two friendly numbers a decimal sits between and find their midpoint.
- I can round a decimal to the nearest whole number.
- I can round a decimal to the nearest tenth and the nearest hundredth.
- I can use the digit to the right of the rounding place to round quickly.
- I can round a case that carries over, such as 3.96 to the nearest tenth being 4.0.
Standards this unit teaches
- 5.NBT.A.4Common Core (US)Round decimals to any place
Use place value understanding to round decimals to any place.
- 5.NBT.A.3Common Core (US)Read and compare decimals (foundation)
Read, write and compare decimals to thousandths using base-ten numerals, number names and expanded form, and compare using >, = and < symbols. Deciding which friendly number a decimal is nearer to rests on this comparing.
- AC9M5N04Australian Curriculum v9 (ACARA)Decimals with estimation and rounding (Year 5)
Use place value to add and subtract decimals, with estimation and rounding to check that answers are reasonable. Rounding decimals is named directly inside this Year 5 descriptor.
- AC9M4N01Australian Curriculum v9 (ACARA)Place value to tenths and hundredths (Year 4)
Extend place value to tenths and hundredths and use decimal notation to name and represent these numbers. This decimal place-value understanding is the foundation the rounding work rests on.
Prior knowledge
This unit builds on skills students should already have met. Revisit any that are shaky first.
- Grade 5 decimals to tenths and hundredths teaching unitreading decimal place value, which rounding depends on
- Grade 3 rounding and place value teaching unitrounding whole numbers on a number line, the same distance idea
- Grade 4 place value teaching uniteach place worth ten of the place to its right, now past the decimal point
- How to teach roundingswapping a number for the nearest friendly one
- The number linereading where a point sits between two marks
Words to teach and display
- Decimal
- a number with a decimal point, with tenths, hundredths and thousandths to the right of it
- Place value
- the value a digit has by its position, so the 4 in 3.47 means 4 tenths
- Tenths
- the first place after the decimal point, one tenth of a whole
- Hundredths
- the second place after the decimal point, one tenth of a tenth
- Round
- to swap a decimal for the nearest friendly whole, tenth or hundredth
- Midpoint
- the number exactly halfway between the two friendly numbers, such as 3.5 between 3 and 4
Teach it: concrete, pictorial, abstract
The lesson moves from things students can hold, to pictures and diagrams, to the written maths. The diagrams below are drawn from data, so they are accurate and print cleanly. Teach straight from them.
1. Rounding to the nearest whole number
PictorialTo round 3.7 to the nearest whole number, draw a short number line from 3.0 to 4.0 and find where 3.7 sits. The question is which whole it is nearer to, 3 or 4. Mark the midpoint, 3.5, exactly halfway. Because 3.7 is past the midpoint, it is nearer to 4. So 3.7 rounds to 4. Keeping the line short, just from 3 to 4, makes the nearer end easy to see.
The midpoint is the whole secret of rounding, exactly as it was for whole numbers. Anything past the halfway mark is nearer the higher number, anything before it is nearer the lower one. The distance picture comes first, the digit rule later.
The rule for a tie, landing exactly on the midpoint, is to round up. So 3.5 rounds to 4. This is the standard convention, and it keeps the rule simple and consistent.
Round 12.47 to the nearest whole number.
- 12.47 sits between 12 and 13.
- The midpoint is 12.5.
- 12.47 is before the midpoint, so it is nearer to 12.
Answer: 12.47 rounds to 12.
- Which two whole numbers does 3.7 sit between, and where is the midpoint?
- Round 8.2 to the nearest whole number. Is it before or after the midpoint?
2. Rounding to the nearest tenth
PictorialRounding to the nearest tenth works the same way, just zoomed in. To round 3.47 to the nearest tenth, the two friendly tenths on either side are 3.4 and 3.5. Draw a line from 3.4 to 3.5 with the midpoint 3.45 marked. Because 3.47 is past 3.45, it is nearer to 3.5, so 3.47 rounds to 3.5. The line only shows the range that matters, so the decimals do not crowd the view.
Notice the ticks here are hundredths (3.41, 3.42, and so on), but only the ends and the midpoint are labelled so the picture stays clean. The two friendly numbers to round to, 3.4 and 3.5, sit at the ends.
Zooming the line to a single tenth is the key habit. Rounding to a tenth is a decision between two neighbouring tenths, so the line should run from one to the next, never across a wide range.
Round $3.66 to the nearest tenth of a dollar (nearest ten cents).
- 3.66 sits between 3.6 and 3.7.
- The midpoint is 3.65.
- 3.66 is past the midpoint, so it is nearer to 3.7.
Answer: $3.66 rounds to $3.70.
- Which two tenths does 3.47 sit between, and what is the midpoint?
- Round 5.83 to the nearest tenth. Which tenth is it nearer?
3. Rounding to the nearest hundredth
PictorialZoom in once more for the nearest hundredth. To round 3.472 to the nearest hundredth, the two friendly hundredths on either side are 3.47 and 3.48. The line runs from 3.47 to 3.48 with the midpoint 3.475 marked. This time 3.472 is before the midpoint, so it is nearer to 3.47. So 3.472 rounds down to 3.47. The same distance question, just at a finer scale.
The ticks are now thousandths, but again only the ends and the midpoint are labelled. Rounding to a hundredth is a decision between two neighbouring hundredths, so the line spans exactly one hundredth, from 3.47 to 3.48.
It does not matter how many digits trail after, only which side of the midpoint the number falls. 3.472 and 3.474 both round to 3.47, while 3.476 and 3.478 both round to 3.48.
Round 3.478 to the nearest hundredth.
- 3.478 sits between 3.47 and 3.48.
- The midpoint is 3.475.
- 3.478 is past the midpoint, so it is nearer to 3.48.
Answer: 3.478 rounds to 3.48.
- Which two hundredths does 3.472 sit between, and what is the midpoint?
- Round 2.834 to the nearest hundredth. Which side of the midpoint is it?
4. The digit rule and cases that carry over
AbstractOnce the number line makes sense, the fast version is the digit rule. To round to a place, look only at the one digit immediately to its right. If that digit is 5 or more, round up; if it is 4 or less, round down. This works because that digit tells you which side of the midpoint you are on, which is exactly what the line showed.
To round 3.47 to the nearest tenth, look at the digit right of the tenths place, the 7. Since 7 is 5 or more, round the tenths up: 3.5. That is the same answer the line gave, found in one glance.
Watch the carry-over cases. Rounding 3.96 to the nearest tenth: the digit to the right is 6, so round the 9 up. But 9 tenths rounding up rolls into the next whole, so 3.96 becomes 4.0, not 3.10. And keep any place-holding zero: 3.7 rounded to the nearest hundredth is 3.70, because the hundredths place must be shown.
Round 3.96 to the nearest tenth using the digit rule.
- The rounding place is the tenths, the 9. Look one digit to the right: the 6.
- 6 is 5 or more, so round the tenths up.
- 9 tenths plus 1 rolls over: the 3.9 becomes 4.0.
Answer: 3.96 rounds to 4.0. The carry moves it up a whole number.
- To round 5.83 to the nearest tenth, which single digit do you look at?
- Why does 3.96 round to 4.0 rather than 3.10?
Common misconceptions and how to address them
MisconceptionThe more decimal places a number has, the bigger it is, so 3.47 is bigger than 3.5.
Why it happens: Students read 47 as larger than 5 and forget the places line up by value, not by length.
How to address it: Line the numbers up by place: 3.5 is 3.50, and 50 hundredths beat 47 hundredths. Put both on the number line and 3.5 sits to the right of 3.47.
MisconceptionRounding to fewer places means chopping off the extra digits, so 3.47 to the nearest tenth is 3.4.
Why it happens: Students truncate rather than round, dropping the digits instead of deciding nearer.
How to address it: Rounding is a nearer-to decision, not a chop. 3.47 is past the midpoint 3.45, so it rounds up to 3.5, not down to 3.4. Truncating would ignore where the number actually sits.
MisconceptionRound one digit at a time from the right, so 3.749 to the nearest tenth becomes 3.75 then 3.8.
Why it happens: Students chain rounds, rounding to hundredths first and then to tenths.
How to address it: Round in one step, looking only at the single digit right of the target place. For the nearest tenth of 3.749 look at the 4: it is 4 or less, so 3.749 rounds to 3.7, not 3.8.
MisconceptionWhen the rounding digit is 9 and rounds up, write a 10 in that place, so 3.96 to the nearest tenth is 3.10.
Why it happens: Students add one to the 9 without carrying into the next place.
How to address it: Nine tenths plus one tenth is a whole ten tenths, which carries. 3.9 rounds up to 4.0. On the line, 3.96 is between 3.9 and 4.0 and nearer 4.0.
MisconceptionDrop the trailing zero after rounding, so 3.70 becomes 3.7 when the nearest hundredth was wanted.
Why it happens: The zero looks like it adds nothing, so students remove it.
How to address it: The place you rounded to must be shown. Rounded to the nearest hundredth, the answer needs a hundredths digit, so it is 3.70. The zero holds the place and says the rounding went to hundredths.
MisconceptionLook at all the digits to the right, not just the next one, so 3.42 rounds the tenth up because there is a 2.
Why it happens: Students think any non-zero digit to the right pushes the round up.
How to address it: Only the single digit immediately right of the rounding place decides it. For the nearest tenth of 3.42 that digit is 2, which is 4 or less, so it rounds down to 3.4.
Guided practice (with answers)
1. Round 3.7 to the nearest whole number.
3.7 is past 3.5, so it rounds to 4. Answer: 4. It is between 3 and 4, past the midpoint 3.5, so nearer 4.
2. Round 3.47 to the nearest tenth.
3.47 is past 3.45, so it rounds to 3.5. Answer: 3.5. It is between 3.4 and 3.5, past the midpoint 3.45.
3. Round 3.472 to the nearest hundredth.
Answer: 3.47. It is between 3.47 and 3.48, before the midpoint 3.475.
4. Round $12.47 to the nearest dollar.
Answer: $12. It is between 12 and 13, before the midpoint 12.5.
5. Round 3.96 to the nearest tenth.
Answer: 4.0. The 6 rounds the 9 tenths up, which carries to a whole.
6. Round 5.834 to the nearest hundredth.
Answer: 5.83. The digit to the right is 4, which is 4 or less, so round down.
Independent practice worksheets
Set the matching ChalkBee worksheets for independent work. The answer keys are computed in code, so they are never wrong. Start with the rounding sets for decimals, then use the estimation sets to apply rounding to checking answers.
Differentiation
- Give a pre-drawn number line for the target place with the midpoint already marked, so the student only plots the number and reads the nearer end.
- Start with rounding to the nearest whole, where the friendly numbers are ordinary whole numbers, before moving to tenths and hundredths.
- Provide the two friendly numbers as a fill-in, such as 'between ___ and ___', so the student focuses on the nearer decision.
- Rewrite the decimal with a trailing zero (3.5 as 3.50) when comparing, so the places line up column by column.
- Round 3.749 to the nearest whole, tenth and hundredth and explain why the three answers can differ.
- Find a decimal that rounds to 4 as a whole number but to 3.5 as a tenth, and show why.
- Explain, using the number line, why the exact-half convention rounds 3.5 up to 4 rather than down to 3.
- Round a measurement two ways for a real task, such as a plank at 3.472 m to the nearest centimetre and to the nearest tenth of a metre.
Assessment: exit ticket
A three-question exit ticket for the last five minutes. It samples rounding to a whole, to a tenth, and a carry-over case.
1. Round 7.62 to the nearest whole number.
Answer: 8. It is between 7 and 8, past the midpoint 7.5.
2. Round 4.83 to the nearest tenth.
Answer: 4.8. The digit to the right is 3, which is 4 or less, so round down.
3. Round 2.97 to the nearest tenth.
Answer: 3.0. The 7 rounds the 9 tenths up, which carries to a whole.
Teacher notes and timings
- Rough timing across three to four lessons: Lesson 1 rounding to the nearest whole on a number line (section 1), Lesson 2 the nearest tenth (section 2), Lesson 3 the nearest hundredth (section 3), Lesson 4 the digit rule and carry-over cases plus the exit ticket (section 4).
- Every rounding number line here is deliberately zoomed to a single unit of the target place, from one friendly number to the next, with only the two ends and the midpoint labelled. This keeps the which-is-it-nearer decision visual and stops the decimals from crowding. Teach the distance question first, then the digit rule as its fast form.
- The most stubborn misconception is that more decimal places means a bigger number (3.47 seeming bigger than 3.5). Line the numbers up by place, write 3.5 as 3.50, and plot both on the line to defeat it.
- Rounding is a nearer-to decision, not a chop. Students who truncate will round 3.47 down to 3.4. Keep coming back to the midpoint on the line so they decide by distance, not by deleting digits.
- Rehearse the two edge behaviours on purpose: the carry-over (3.96 to the nearest tenth is 4.0, not 3.10) and the place-holding zero (3.7 to the nearest hundredth is 3.70). Both follow straight from place value.
- US and AU alignment: the US names rounding decimals to any place at Grade 5 (5.NBT.A.4), building on reading and comparing decimals (5.NBT.A.3). ACARA names rounding decimals directly inside the Year 5 decimals descriptor (AC9M5N04), resting on the tenths and hundredths place value introduced at Year 4 (AC9M4N01). The number-line method here serves both.
- Present mode and print both work: use the Print button for a clean handout, or project the number lines and plot the decimals with the class straight from the diagrams.