🔢 Place Value & Rounding

Grade 5 · Number · Cambridge Primary Stage 5

Place Value

Millions, thousands, hundreds, tens, ones

Ordering Numbers

Comparing with < and >

Rounding

To 10, 100, 1000 and beyond

Negative Numbers

Below zero on a number line

Roman Numerals

I, V, X, L, C, D, M

1. Place Value

Every digit in a number has a place value — the position of the digit tells you how much it is worth.

MillionsHundred ThousandsTen ThousandsThousandsHundredsTensOnes
3472506
The number 3,472,506 means:
3 × 1,000,000 = 3,000,000
4 × 100,000 = 400,000
7 × 10,000 = 70,000
2 × 1,000 = 2,000
5 × 100 = 500
0 × 10 = 0
6 × 1 = 6
💡 We use commas to separate groups of three digits: 3,472,506. This makes big numbers easier to read!

2. Ordering & Comparing Numbers

To compare numbers, look at the digits from left to right. The first digit where they differ tells you which is bigger.

Compare 47,382 and 47,519:
Both start 4, 7 — same.
Next digit: 3 vs 5. Since 3 < 5, we have 47,382 < 47,519
< means "less than"  |  > means "greater than"  |  = means "equal to"
💡 To order a list of numbers, compare them two at a time. Start with the leftmost digit and work right.

3. Rounding Numbers

Rounding makes numbers easier to work with. We round to the nearest 10, 100, 1000 etc.

Look at the digit to the RIGHT of your rounding position.
If it's 0, 1, 2, 3, 4 → round DOWN (keep the digit the same)
If it's 5, 6, 7, 8, 9 → round UP
Round 7,348 to the nearest 100:
Hundreds digit = 3. Look at tens digit = 4. Since 4 < 5 → round down.
7,348 ≈ 7,300
Round 7,368 to the nearest 100:
Hundreds digit = 3. Look at tens digit = 6. Since 6 ≥ 5 → round up.
7,368 ≈ 7,400
💡 The symbol ≈ means "approximately equal to".

4. Negative Numbers

Negative numbers are below zero. They are written with a minus sign: −3, −15, −100.

← smaller    −5   −4   −3   −2   −1   0   1   2   3   4   5    larger →
Examples:
−8 < −3 (−8 is further left, so smaller)
−2 > −7
Temperature: −5°C is colder than −1°C
💡 On a number line, numbers always increase from left to right. Negative numbers are to the left of zero.

5. Roman Numerals

SymbolIVXLCDM
Value1510501005001000
Rules:
Add symbols from left to right: VIII = 5+1+1+1 = 8
Subtract when a smaller value comes before a larger: IV = 5−1 = 4, IX = 10−1 = 9, XL = 40, XC = 90, CD = 400, CM = 900
XIV = 10 + (5−1) = 14  |  XL = 40  |  XLVIII = 48
MCMXCIX = 1000 + (1000−100) + (100−10) + (10−1) = 1999

Example 1 — Reading Place Value

In the number 285,634, what is the value of the digit 8?

Position: 8 is in the ten-thousands place.
Value: 8 × 10,000 = 80,000

Example 2 — Rounding to the Nearest 1000

Round 56,450 to the nearest 1000.

Thousands digit: 6
Look at hundreds digit: 4. Since 4 < 5, round down.
Answer: 56,000

Example 3 — Rounding to the Nearest 10

Round 7,865 to the nearest 10.

Tens digit: 6
Look at ones digit: 5. Since 5 ≥ 5, round up.
Answer: 7,870

Example 4 — Ordering Negative Numbers

Order from smallest to largest: −3, 5, −8, 0, 2

On a number line: −8 is furthest left, then −3, then 0, then 2, then 5.
Answer: −8, −3, 0, 2, 5

🔢 Place Value Exploder

🔵 Rounding Machine

🌡️ Number Line

Exercise 1 — Place Value

1. In 374,521 what is the value of the 3?

2. In 85,046 what is the value of the 8?

3. In 603,718 what digit is in the thousands place?

4. Write the value of the 5 in 1,250,000.

5. In 947,283, what is the ten-thousands digit?

6. What is 400,000 + 70,000 + 3,000 + 200 + 50 + 8?

7. Write 3 × 100,000 + 5 × 10,000 + 2 × 1,000 + 7 × 10 + 4 as a number.

8. In 2,805,134, how many thousands are there in total? (Think: full thousands in the number)

9. Write the number: two hundred and forty thousand, six hundred and three.

10. What is the largest 6-digit number you can make using the digits 3, 8, 1, 9, 4, 6 (each once)?

Exercise 2 — Rounding to 10 and 100

1. Round 47 to the nearest 10.

2. Round 83 to the nearest 10.

3. Round 155 to the nearest 10.

4. Round 4,385 to the nearest 100.

5. Round 7,250 to the nearest 100.

6. Round 99,941 to the nearest 100.

7. Round 845 to the nearest 10.

8. Round 3,651 to the nearest 100.

9. Round 29,975 to the nearest 100.

10. Round 5,050 to the nearest 100.

Exercise 3 — Rounding to 1,000 and 10,000

1. Round 8,372 to the nearest 1,000.

2. Round 15,500 to the nearest 1,000.

3. Round 249,499 to the nearest 1,000.

4. Round 63,400 to the nearest 10,000.

5. Round 87,500 to the nearest 10,000.

6. Round 345,678 to the nearest 10,000.

7. Round 4,499 to the nearest 1,000.

8. Round 995,001 to the nearest 1,000.

9. Round 749,999 to the nearest 100,000.

10. Round 1,450,000 to the nearest 100,000.

Exercise 4 — Ordering & Negative Numbers

1. Which is larger: 48,295 or 48,312? Enter 1 for first, 2 for second.

2. Which is smaller: −4 or −9? Enter the smaller value.

3. Put in order (smallest first). Enter the 3rd value: 3, −5, 0, −2, 7

4. What number is exactly halfway between −6 and 4?

5. Temperature is −3°C. It rises 8°C. New temperature?

6. Which is larger: 999,999 or 1,000,000? Enter 1 or 2.

7. What integer comes just before −10?

8. What is the difference between −5 and 3?

9. Order smallest to largest. Enter the 2nd value: 45,300; 45,030; 45,003; 45,300

10. A submarine is at −200 m. It rises 75 m. New depth?

Exercise 5 — Roman Numerals

1. What is XIV in numerals?

2. What is XL in numerals?

3. What is XCIX in numerals?

4. What is CDXLVII in numerals?

5. What is MCMLXXXIV in numerals?

6. Write 24 in Roman numerals. Enter as a number: how many symbols does XXIV use? (Just enter 24)

7. Write 49 in Roman numerals value check: XLIX = ?

8. What is MMI in numerals?

9. What is DCCC in numerals?

10. What is MMXXV in numerals?

🏋️ Practice — 20 Questions

1. Value of 6 in 362,850?

2. Round 7,845 to nearest 1,000.

3. Round 34,550 to nearest 10,000.

4. Round 489 to nearest 100.

5. What is −7 + 10?

6. Which is greater: −12 or −8? Enter the greater value.

7. Write 500,000 + 40,000 + 800 + 7 as a number.

8. Round 2,950 to nearest 100.

9. What is LXXVII in numerals?

10. Temperature −6°C falls 4°C. New temp?

11. Value of 9 in 190,345?

12. Round 654,321 to nearest 100,000.

13. What integer is halfway between −8 and −2?

14. MCMXCV = ?

15. Round 45 to nearest 10.

16. Write 4,000,000 + 300,000 + 20,000 + 5,000 + 600 + 70 + 8.

17. What is the difference between 5 and −3?

18. Round 5,555 to nearest 10.

19. In 7,028,415 what digit is in the hundred-thousands place?

20. What is CDXCIX in numerals?

🏆 Challenge — 8 Questions

1. A number rounds to 45,000 when rounded to the nearest 1,000. What is the smallest it could be?

2. A number rounds to 45,000 to nearest 1,000. What is the largest it could be?

3. Using digits 2, 5, 8, 0, 4, 7 (each once), what is the largest number closer to 800,000 than 900,000?

4. What year is MCMLXIX?

5. Three numbers have a mean of 0. Two are −5 and 7. What is the third?

6. A number has 5 in the ten-thousands place, 3 in the millions place, and 0 everywhere else. What is the number?

7. If you round 7,849,500 to the nearest 100,000, what do you get?

8. What is the next Roman numeral year after MMXXV?