Number · Number and Numeration Systems · Lesson 4
Rounding Decimals to Tenths, Hundredths and Thousandths
Fuel prices, exchange rates and science measurements often have many digits after the decimal point, but our money only goes down to the pesewa (one hundredth of a cedi). In this lesson you will round decimals to the nearest tenth, hundredth and thousandth, and learn how rounding up, rounding down and rounding off work with decimals.
By the end you will be able to
- ✔Name the tenths, hundredths and thousandths places in a decimal.
- ✔Round off decimals to the nearest tenth, hundredth and thousandth.
- ✔Round decimals up and down to a given place and explain the difference from rounding off.
- ✔Keep necessary zeros (e.g. 78.460, 13.00) when rounding.
Key words
- Tenth
- The first place after the decimal point; one tenth = 0.1 = .
- Hundredth
- The second place after the decimal point; one hundredth = 0.01 = . One pesewa is a hundredth of a cedi.
- Thousandth
- The third place after the decimal point; one thousandth = 0.001 = .
- Round off
- Choose the NEAREST value at the chosen place.
- Round up / round down
- Choose the LARGER / SMALLER of the two possible values at the chosen place.
Curriculum reference
Content standard: B7.1.1.1 Demonstrate understanding and the use of place value for expressing quantities recorded as base ten numerals as well as rounding these to given decimal places and significant figures.
Indicator: Round decimals to the nearest tenth, hundredth, thousandths, etc.
Starter
Paying for fuel to the pesewa
At a filling station in Takoradi the pump shows that petrol costs GH₵14.678 per litre. But there is no coin smaller than one pesewa (GH₵0.01), so nobody can pay exactly GH₵14.678! The station must round the price to the nearest pesewa. Should it be GH₵14.67 or GH₵14.68? This lesson shows you how to decide — and why both the driver and the station owner care.
1. Decimal places: tenths, hundredths, thousandths
You already know that each place in a whole number is 10 times the place on its right. The same pattern continues after the decimal point, but now each place is one tenth of the place on its left. The first place after the point is tenths, then hundredths, then thousandths, then ten-thousandths.
| Hundreds | Tens | Ones | . | Tenths | Hundredths | Thousandths | Ten-thousandths |
|---|---|---|---|---|---|---|---|
| 4 | 8 | 6 | . | 3 | 6 | 8 | 5 |
▶ See how the value of each digit after the point gets ten times smaller as you move right.
So in 486.3685 the 3 is worth 3 tenths (0.3), the 6 is worth 6 hundredths (0.06) and the 8 is worth 8 thousandths (0.008). Rounding to the nearest tenth means rounding to 1 decimal place, nearest hundredth means 2 decimal places, and nearest thousandth means 3 decimal places.
2. Rounding off decimals
Rounding decimals works exactly like rounding whole numbers. The number lies between two values at the chosen place, and rounding off picks the nearer one. The deciding digit is the digit just to the right of the rounding place.
- 1Find the digit in the rounding place (tenths, hundredths or thousandths).
- 2Look at the deciding digit immediately to its right.
- 30, 1, 2, 3 or 4 → keep the rounding digit. 5, 6, 7, 8 or 9 → add 1 to it (carry if it is 9).
- 4Drop all the digits after the rounding place. (Unlike whole numbers, we do NOT replace them with zeros — the decimal point already keeps the size.)
▶ Zooming in between two hundredths: notice that 486.3685 is past the halfway mark.
| Number | Nearest tenth | Nearest hundredth | Nearest thousandth |
|---|---|---|---|
| 486.3685 | 486.4 | 486.37 | 486.369 |
| 0.0605368 | 0.1 | 0.06 | 0.061 |
Look carefully at 0.0605368. To the nearest tenth, the tenths digit is 0 and the deciding digit is 6, so 0 becomes 1 and the answer is 0.1. To the nearest hundredth, the hundredths digit is 6 and the deciding digit is 0, so it stays: 0.06. To the nearest thousandth, the thousandths digit is 0 and the deciding digit is 5, so it becomes 0.061.
3. Rounding decimals up and down
Just as with whole numbers, round up means take the larger of the two possible values and round down means take the smaller — whatever the deciding digit is. Round off uses the deciding digit to find the nearer value. Let us round 78.4604783.
| 78.4604783 to the nearest… | Round up | Round off | Round down |
|---|---|---|---|
| tenth | 78.5 | 78.5 | 78.4 |
| hundredth | 78.47 | 78.46 | 78.46 |
| thousandth | 78.461 | 78.460 | 78.460 |
▶ Round up and round down simply choose an end; round off chooses the nearer end.
4. Zeros that must stay
When you round to a given place, your answer must have exactly that many decimal places — even if the last digit is a zero. 78.4604783 to the nearest thousandth is 78.460, not 78.46. The final 0 tells the reader that the number is accurate to the thousandths place.
Worked examples
Try each one yourself first, then open the solution and compare every step.
Example 1
Three places for one number
Show the solution
- Step 1(a) Tenths digit 3; deciding digit 6 (5 or more) → 3 becomes 4: 486.4.
- Step 2(b) Hundredths digit 6; deciding digit 8 → 6 becomes 7: 486.37.
- Step 3(c) Thousandths digit 8; deciding digit 5 → 8 becomes 9: 486.369.
Answer: (a) 486.4 (b) 486.37 (c) 486.369
Example 2
A small decimal
Show the solution
- Step 1(a) Tenths digit 0; deciding digit 6 → 0 becomes 1: 0.1.
- Step 2(b) Hundredths digit 6; deciding digit 0 → keep 6: 0.06.
- Step 3(c) Thousandths digit 0; deciding digit 5 → 0 becomes 1: 0.061.
Answer: (a) 0.1 (b) 0.06 (c) 0.061
Example 3
Up, off and down
Show the solution
- Step 1To the nearest tenth, 78.4604783 lies between 78.4 and 78.5.
- Step 2(a) Round up = larger = 78.5.
- Step 3(b) Round off: tenths digit 4, deciding digit 6 (5 or more) → 78.5.
- Step 4(c) Round down = smaller = 78.4.
Answer: (a) 78.5 (b) 78.5 (c) 78.4
Example 4
Fuel price to the nearest pesewa
Show the solution
- Step 1A pesewa is GH₵0.01, so we round to the nearest hundredth (2 decimal places).
- Step 2Hundredths digit 7; deciding digit 8 (5 or more) → 7 becomes 8.
- Step 3Answer: GH₵14.68.
Answer: GH₵14.68
Example 5
Carrying through nines
Show the solution
- Step 1Hundredths digit 9; deciding digit 6 → add 1 to the 9.
- Step 29 + 1 = 10, so write 0 and carry 1 to the tenths: 9 + 1 = 10 again, so carry 1 to the ones: 2 + 1 = 3.
- Step 3The number becomes 13.00 — keep both zeros to show 2 decimal places.
Answer: 13.00
Summary
- After the decimal point the places are tenths, hundredths, thousandths, … each one tenth of the place on its left.
- Round off: look at the deciding digit — 0–4 keep, 5–9 add 1 — then drop the digits after the rounding place.
- Round up takes the larger possible value; round down takes the smaller possible value.
- Keep the right number of decimal places, including end zeros: 78.460, 13.00.
- Money is rounded to the nearest pesewa, i.e. the nearest hundredth of a cedi.
Practice: 15 questions
5 easy, 5 medium, 5 hard. Each one is marked straight away, with a full worked solution.
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