🔍 Decimal Detective: Place Value & Rounding 🕵️

Every digit in a decimal number has a specific value depending on its position. In Grade 6, you'll read and write decimals to 3 decimal places (thousandths), order and compare them, and round decimals with precision. Master place value and you'll unlock confidence in all decimal calculations!

📊 Place Value Chart
3.427 → 3 ones, 4 tenths, 2 hundredths, 7 thousandths
📏 Ordering Decimals
Compare left to right: 3.42 vs 3.38
→ ones same → tenths: 4 > 3 → 3.42 > 3.38
🔄 Rounding Decimals
Round 3.456 to 1 d.p.: look at hundredths (5)
→ round up → 3.5

📜 Golden Rules

🗺️ Rule 1: Place Value Positions

The positions left to right from the decimal point are: tenths (÷10), hundredths (÷100), thousandths (÷1000).

For example, in 3.427:

  • The 4 is in the tenths place → worth 4 tenths = 0.4
  • The 2 is in the hundredths place → worth 2 hundredths = 0.02
  • The 7 is in the thousandths place → worth 7 thousandths = 0.007
Ones.TenthsHundredthsThousandths
3.427

🔢 Rule 2: Ordering Decimals

To order decimals, compare digits from LEFT to RIGHT:

  1. First compare the whole number part.
  2. If equal, compare tenths digits.
  3. If equal, compare hundredths digits.
  4. If equal, compare thousandths digits.

⚠️ Rule 3: Watch Out for Zeros!

Never drop a zero in the middle of a decimal. For example:

  • 3.04 ≠ 3.4  (the zero is a crucial placeholder in the tenths column)

But trailing zeros can be dropped:

  • 3.40 = 3.4  (the trailing zero after 4 adds no value)

🔄 Rule 4: Rounding Rules

  • To the nearest whole number: Look at the tenths digit. 5 or above → round up. Below 5 → round down.
  • To 1 decimal place (1 d.p.): Look at the hundredths digit. 5 or above → round up the tenths. Below 5 → leave tenths unchanged.
  • To 2 decimal places (2 d.p.): Look at the thousandths digit. Same rule: 5 or above → round up, below 5 → round down.

✖️ Rule 5: Multiplying and Dividing by 10, 100, 1000

  • Multiplying by 10/100/1000: digits move LEFT (the number gets bigger).
    e.g., 2.47 × 10 = 24.7   |   2.47 × 100 = 247   |   2.47 × 1000 = 2470
  • Dividing by 10/100/1000: digits move RIGHT (the number gets smaller).
    e.g., 2.47 ÷ 10 = 0.247   |   2.47 ÷ 100 = 0.0247   |   2.47 ÷ 1000 = 0.00247
Collins Stage 6 — Units 9 & 10: Place Value, Ordering & Rounding Decimals 🔍

📖 Worked Examples

Study these step-by-step examples carefully before trying the practice questions.

Example 1: Reading a Place Value Chart

Write 5.083 in a place value chart and explain each digit.

Ones.TenthsHundredthsThousandths
5.083
🔵 5 ones = 5
⚠️ 0 tenths = 0  — this zero is a placeholder. Very important! Without it, 5.083 would become 5.83, which is a different number.
🟠 8 hundredths = 0.08
🟣 3 thousandths = 0.003
✅ Total: 5 + 0 + 0.08 + 0.003 = 5.083

Example 2: Ordering Decimals

Order these from smallest to largest: 4.3, 4.27, 4.305, 4.03

Step 1: All four numbers have 4 ones — so we move on to compare tenths.
Step 2: Tenths digits are: 4.3 → 3,   4.27 → 2,   4.305 → 3,   4.03 → 0
Step 3: 4.03 has 0 tenths → this is the smallest so far.
Step 4: 4.27 has 2 tenths → next smallest.
Step 5: 4.3 and 4.305 both have 3 tenths → compare hundredths: both have 0 hundredths → compare thousandths: 4.3 has 0, 4.305 has 5 → 4.3 < 4.305.
✅ Order (smallest to largest): 4.03, 4.27, 4.3, 4.305

Example 3: Rounding

Round 6.847 to (a) the nearest whole number   (b) 1 d.p.   (c) 2 d.p.

(a) Nearest whole number: Look at the tenths digit → it is 8. Since 8 ≥ 5, round UP.
✅ 7
(b) 1 decimal place: Look at the hundredths digit → it is 4. Since 4 < 5, round DOWN (leave the tenths digit as it is).
✅ 6.8
(c) 2 decimal places: Look at the thousandths digit → it is 7. Since 7 ≥ 5, round UP the hundredths digit from 4 to 5.
✅ 6.85

Example 4: Multiplying and Dividing by 10, 100, 1000

(a) 3.47 × 100   (b) 0.083 × 1000   (c) 56.4 ÷ 10   (d) 7.2 ÷ 1000

(a) 3.47 × 100: Multiply by 100 → digits move 2 places LEFT.
3.47 → 347. → ✅ 347
(b) 0.083 × 1000: Multiply by 1000 → digits move 3 places LEFT.
0.083 → 083. → ✅ 83
(c) 56.4 ÷ 10: Divide by 10 → digits move 1 place RIGHT.
56.4 → 5.64 → ✅ 5.64
(d) 7.2 ÷ 1000: Divide by 1000 → digits move 3 places RIGHT.
7.2 → 0.0072 → ✅ 0.0072
Collins Stage 6 — Units 9 & 10: Place Value, Ordering & Rounding Decimals 🔍

🔬 Place Value Explorer

Enter any decimal number (up to thousandths) and explore its place value, digit breakdown, and rounded versions!

Collins Stage 6 — Units 9 & 10: Place Value, Ordering & Rounding Decimals 🔍

🎯 Drag 1: Place Value of a Digit

In the number 7.358, what is the value of the digit 5?

Ones.TenthsHundredthsThousandths
7.358

💡 Hint: 7 . 3 5 8 → ones . tenths hundredths thousandths. Which position is the 5 in?

5 tenths
5 hundredths
5 thousandths
5 ones

The value of the digit 5 is:

Drop here
Collins Stage 6 — Units 9 & 10: Place Value, Ordering & Rounding Decimals 🔍

🎯 Drag 2: Ordering Decimals

Which is the LARGEST of these decimals?

0.45    0.405    0.504    0.045

💡 Hint: Compare tenths first. Which has the biggest tenths digit?

Tenths digits: 0.45 → 4 | 0.405 → 4 | 0.504 → 5 | 0.045 → 0

0.45
0.405
0.504
0.045

The largest decimal is:

Drop here
Collins Stage 6 — Units 9 & 10: Place Value, Ordering & Rounding Decimals 🔍

🎯 Drag 3: Round to Nearest Whole Number

Round 8.74 to the nearest whole number.

8 . 7 4

ones . tenths hundredths

💡 Hint: Look at the tenths digit. 7 ≥ 5, so round UP!

8
9
10
7

8.74 rounded to the nearest whole number is:

Drop here
Collins Stage 6 — Units 9 & 10: Place Value, Ordering & Rounding Decimals 🔍

🎯 Drag 4: Round to 1 Decimal Place

Round 3.461 to 1 decimal place.

3 . 4 6 1

ones . tenths hundredths thousandths

Look at the hundredths digit (6) to decide whether to round the tenths up or down.

💡 Hint: 6 ≥ 5 → round UP the tenths digit from 4 to 5.

3.4
3.5
3.46
3.47

3.461 rounded to 1 decimal place is:

Drop here
Collins Stage 6 — Units 9 & 10: Place Value, Ordering & Rounding Decimals 🔍

🎯 Drag 5: Multiply by 1000

Calculate 0.047 × 1000

0 . 0 4 7   ×1000 → digits move 3 places LEFT

0 . 0 4 7 → 0 4 7 . = 47

💡 Hint: × 1000 moves digits 3 places to the LEFT. 0.047 → 047 = 47

0.47
4.7
47
470

0.047 × 1000 =

Drop here
Collins Stage 6 — Units 9 & 10: Place Value, Ordering & Rounding Decimals 🔍

🎯 Drag 6: Between on a Number Line

Which decimal is between 3.4 and 3.5?

3.4 between here 3.5

💡 Hint: It must be greater than 3.4 AND less than 3.5.

3.51
3.39
3.47
3.50

The decimal between 3.4 and 3.5 is:

Drop here
Collins Stage 6 — Units 9 & 10: Place Value, Ordering & Rounding Decimals 🔍

✏️ Practice Questions

Answer all 20 questions, then click Show Answers to check your work.

  1. Write the value of the digit 4 in the number 6.423.
  2. Write the value of the digit 7 in 12.073.
  3. Order from smallest to largest:   2.3,   2.03,   2.35,   2.305
  4. Order from largest to smallest:   0.9,   0.09,   0.99,   0.909
  5. Round 4.567 to the nearest whole number.
  6. Round 4.567 to 1 decimal place.
  7. Round 4.567 to 2 decimal places.
  8. Calculate 5.36 × 10
  9. Calculate 0.782 × 100
  10. Calculate 34.5 ÷ 1000
  11. Which is greater: 0.305 or 0.35? Explain how you know.
  12. Write 0.045 in words.
  13. Round 9.995 to 2 decimal places.
  14. Calculate 0.08 × 1000
  15. A marathon runner completes the race in 2.674 hours. Round to 1 decimal place.
  16. Insert < or >:   1.09 ___ 1.1
  17. What is 7.3 ÷ 100?
  18. Round 0.0456 to 2 decimal places.
  19. Order these heights from shortest to tallest:   1.6 m,   1.58 m,   1.605 m,   1.62 m
  20. What number is 0.001 more than 4.999?

✅ Answers

  1. The digit 4 is in the tenths position → its value is 4 tenths = 0.4
  2. The digit 7 is in the thousandths position → its value is 7 thousandths = 0.007
  3. Smallest to largest: 2.03, 2.3, 2.305, 2.35
    (Compare tenths: 0, 3, 3, 3 → 2.03 first; then compare hundredths for remaining: 0, 0, 5 → 2.3 = 2.300 and 2.305 next then 2.35)
  4. Largest to smallest: 0.99, 0.909, 0.9, 0.09
  5. Tenths digit is 5 → round up → 5
  6. Hundredths digit is 6 → round up the tenths from 5 to 6 → 4.6
  7. Thousandths digit is 7 → round up the hundredths from 6 to 7 → 4.57
  8. 5.36 × 10 = 53.6 (digits move 1 place left)
  9. 0.782 × 100 = 78.2 (digits move 2 places left)
  10. 34.5 ÷ 1000 = 0.0345 (digits move 3 places right)
  11. 0.35 is greater. Tenths: 3 = 3. Hundredths: 5 > 0. So 0.35 > 0.305.
  12. Forty-five thousandths
  13. Thousandths digit is 5 → round up the hundredths from 9 to 10 → carry over: 9.995 rounds up to 10.00 (or just 10)
  14. 0.08 × 1000 = 80
  15. Hundredths digit is 7 → round up the tenths from 6 to 7 → 2.7 hours
  16. 1.09 < 1.1   (tenths: 0 < 1)
  17. 7.3 ÷ 100 = 0.073
  18. Thousandths digit is 5 → round up hundredths from 4 to 5 → 0.05
  19. Shortest to tallest: 1.58 m, 1.6 m, 1.605 m, 1.62 m
    (1.6 = 1.600; compare hundredths: 1.600 vs 1.605 → thousandths decides; 1.605 < 1.62 since hundredths 0 < 2)
  20. 4.999 + 0.001 = 5.000 = 5
Collins Stage 6 — Units 9 & 10: Place Value, Ordering & Rounding Decimals 🔍

🏆 Challenge Problems

These problems require deeper thinking. Show all working and reasoning!

  1. A scientist measures a sample as 0.347 g. Another scientist measures it as 0.35 g. Which measurement is heavier? By how much?
  2. A number rounded to 1 decimal place gives 3.8. Write three possible values this number could be.
  3. Three runners finish a race in times 12.345 s, 12.3 s and 12.35 s. Place them in finishing order (fastest first).
  4. A decimal number has 3 decimal places. The ones digit is 3, the tenths digit is 2, the hundredths digit is 5, and the thousandths digit is 8. Write the number, then round it to 1 d.p. and 2 d.p.
  5. Round 5.4549 to:
    (a) the nearest whole number   (b) 1 d.p.   (c) 2 d.p.   (d) 3 d.p.
  6. A fabric shop sells material at £12.99 per metre. A customer buys 3.5 metres. Estimate the total cost by first rounding the price to the nearest pound.
  7. What is the difference between the largest and smallest of these decimals: 0.7, 0.07, 0.007, 0.77?
  8. A decimal number rounded to 2 decimal places is 4.50. What is the smallest possible original number?
  9. A number is written as 7._ where the blank is a single digit (0–9). What whole numbers could this number round to? List all possibilities.
  10. A number line goes from 4 to 5. The points 4.25, 4.5, and 4.75 are marked. Between which two marked points does 4.6 lie?

✅ Challenge Answers

  1. 0.35 is heavier.
    Compare: 0.350 vs 0.347 → hundredths: 5 > 4 → 0.35 > 0.347.
    Difference: 0.350 − 0.347 = 0.003 g
  2. A number that rounds to 3.8 to 1 d.p. lies in the range 3.75 ≤ x < 3.85.
    Three possible values: 3.75, 3.80, 3.84 (any value in range accepted)
  3. Fastest (smallest time) first:
    Compare: 12.3 = 12.300 | 12.345 | 12.35 = 12.350
    Order: 12.3 s, 12.345 s, 12.35 s
  4. The number is 3.258
    Rounded to 1 d.p.: hundredths digit is 5 → round up → 3.3
    Rounded to 2 d.p.: thousandths digit is 8 → round up → 3.26
  5. Rounding 5.4549:
    (a) Tenths digit = 4 < 5 → round down → 5
    (b) Hundredths digit = 5 ≥ 5 → round up tenths from 4 to 5 → 5.5
    (c) Thousandths digit = 4 < 5 → round down → 5.45
    (d) 4th decimal digit = 9 ≥ 5 → round up thousandths from 4 to 5 → 5.455
  6. Round £12.99 to nearest pound → £13
    Estimated cost: £13 × 3.5 = £13 × 3 + £13 × 0.5 = £39 + £6.50 = £45.50
  7. Largest: 0.77   Smallest: 0.007
    Difference: 0.770 − 0.007 = 0.763
  8. For a number to round to 4.50 at 2 d.p., the thousandths digit must be 5 or above (to round up), or the number could be exactly 4.495 (since the 5 in the thousandths place rounds up the hundredths from 4 to 5, giving 4.50).
    The smallest possible original number is 4.495.
  9. Numbers of the form 7.0 to 7.4 → tenths digit < 5 → rounds down to 7
    Numbers of the form 7.5 to 7.9 → tenths digit ≥ 5 → rounds up to 8
    So the possible rounded whole numbers are 7 and 8.
  10. 4.6 is greater than 4.5 and less than 4.75.
    Therefore 4.6 lies between 4.5 and 4.75.
Collins Stage 6 — Units 9 & 10: Place Value, Ordering & Rounding Decimals 🔍