Math worksheet for practicing place value up to three decimal places, featuring exercises on identifying digit values, filling in missing numbers, and solving a riddle with decimal clues.

Let's solve each part of this "Place Value to 3DP Sheet 6" step by step.

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A) Write down the value of the underlined digit in each of the numbers below.

We need to determine the value of the underlined digit (i.e., its place value).

1) 34.526 → 0.5
- The underlined digit is 5, which is in the tenths place.
- So, its value is 0.5 ✔

2) 7.832 →
- Underlined digit: 8 → tenths place
- Value = 0.8

3) 23.594 →
- Underlined digit: 5 → tenths place
- Value = 0.5

4) 742.391 →
- Underlined digit: 3 → tenths place
- Value = 0.3

5) 931.372 →
- Underlined digit: 7 → hundredths place
- Value = 0.07

6) 18293.726 →
- Underlined digit: 7 → tenths place
- Value = 0.7

7) 26371.659 →
- Underlined digit: 6 → tenths place
- Value = 0.6

8) 73298.327 →
- Underlined digit: 3 → tenths place
- Value = 0.3

9) 328371.648 →
- Underlined digit: 8 → thousandths place
- Value = 0.008

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✔ A) Answers:
1) 0.5
2) 0.8
3) 0.5
4) 0.3
5) 0.07
6) 0.7
7) 0.6
8) 0.3
9) 0.008

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B) Fill in the missing numbers.

We'll solve each equation one by one.

1) 6 + 0.7 + 0.05 + 0.002 = ?
→ 6 + 0.7 = 6.7
→ 6.7 + 0.05 = 6.75
→ 6.75 + 0.002 = 6.752

2) 7 + ____ = 7.56
→ 7.56 - 7 = 0.56

3) 8.327 = 8 + 0.3 + ____ + 0.007
→ 8 + 0.3 = 8.3
→ 8.327 - 8.3 = 0.027
→ But we already have 0.007 at the end, so:
→ 0.027 - 0.007 = 0.02
→ So missing number is 0.02

4) ____ = 9 + 0.3 + 0.06 + 0.001
→ 9 + 0.3 = 9.3
→ 9.3 + 0.06 = 9.36
→ 9.36 + 0.001 = 9.361

5) 8 + ____ = 8.651
→ 8.651 - 8 = 0.651

6) 7.5 + ____ = 7.514
→ 7.514 - 7.5 = 0.014

7) 9 + 0.327 = ?
→ 9 + 0.327 = 9.327

8) ____ = 5 + 0.007
→ 5 + 0.007 = 5.007

9) 0.3 + 0.008 = ?
→ 0.3 + 0.008 = 0.308

10) 0.7 + 0.06 + 5 = ?
→ 0.7 + 0.06 = 0.76
→ 0.76 + 5 = 5.76

11) 7.34 = 0.04 + ____
→ 7.34 - 0.04 = 7.30

12) ____ + 6 + 0.4 = 6.47
→ 6 + 0.4 = 6.4
→ 6.47 - 6.4 = 0.07

13) 8 + ____ + 0.003 = 8.823
→ 8 + 0.003 = 8.003
→ 8.823 - 8.003 = 0.82

14) 0.09 + ____ = 1.29
→ 1.29 - 0.09 = 1.20

15) 6.392 = 6.002 + ____
→ 6.392 - 6.002 = 0.390

16) ____ = 5 + 0.002 + 0.36
→ 5 + 0.36 = 5.36
→ 5.36 + 0.002 = 5.362

17) 2 + 0.057 + ____ = 2.157
→ 2 + 0.057 = 2.057
→ 2.157 - 2.057 = 0.100

18) ____ + 6 + 0.04 = 6.241
→ 6 + 0.04 = 6.04
→ 6.241 - 6.04 = 0.201

19) 7.327 = ____ + 7 + 0.007
→ 7 + 0.007 = 7.007
→ 7.327 - 7.007 = 0.320

20) 6.24 + ____ = 6.248
→ 6.248 - 6.24 = 0.008

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✔ B) Answers:
1) 6.752
2) 0.56
3) 0.02
4) 9.361
5) 0.651
6) 0.014
7) 9.327
8) 5.007
9) 0.308
10) 5.76
11) 7.30
12) 0.07
13) 0.82
14) 1.20
15) 0.390
16) 5.362
17) 0.100
18) 0.201
19) 0.320
20) 0.008

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C) Work out the answer from the clues.

Let’s go through each clue carefully.

> I am a positive number less than 10.
→ So it's between 0 and 10.

> I have three decimal places.
→ So it's like X.XXX

> My ones digit is an even number.
→ Ones digit: 0, 2, 4, 6, or 8

> If you round me to the nearest whole number, I am 9.
→ So the number is ≥ 8.5 and < 9.5
→ Because rounding to nearest whole number gives 9
→ So number ∈ [8.5, 9.5)

> My tenths digit has the lowest value.
→ Tenths digit is the first decimal place
→ "Lowest value" likely means 0, since digits go from 0–9

> My hundredths digit is the same as my ones digit.
→ So if ones digit is e.g. 8, then hundredths digit is also 8

> My thousandths digit is 4 more than my tenths digit.

Now let’s combine:

- Number is between 8.5 and 9.5 → so ones digit is 8 or 9
- But ones digit must be even → so ones digit = 8
- So number is 8.XXX
- Hundredths digit = ones digit → so hundredths digit = 8
- Tenths digit has lowest value → so tenths digit = 0
- Thousandths digit = tenths digit + 4 → 0 + 4 = 4

So the number is:

- 8.084

Let’s verify all clues:

1. Positive, less than 10 → ✔
2. Three decimal places → ✔
3. Ones digit is even → 8 → ✔
4. Round to nearest whole number → 8.084 → rounds to 8, not 9 ✘

Wait! This is a problem.

But earlier we said it must be ≥8.5 to round to 9.

But 8.084 rounds to 8, not 9 → ✘

Contradiction!

So something is wrong.

Let’s re-express:

We said:
- Rounds to 9 → so number ≥ 8.5 and < 9.5 → so ones digit could be 8 or 9
- But ones digit is even → so only possibility is 8
- But if ones digit is 8, number is like 8.xxx
- To round to 9, the number must be ≥ 8.5
- So tenths digit must be 5 or more

But clue says: "My tenths digit has the lowest value"

What does “lowest value” mean?

Possibility 1: It means 0 → but then number would be ≤ 8.0xx → rounds to 8 → contradiction

Possibility 2: Maybe "lowest value" means smallest possible among digits — but that doesn't make sense.

Wait — perhaps “lowest value” refers to numerical value, meaning it's the smallest digit present? But that’s ambiguous.

Alternatively, maybe “lowest value” means 0, but that leads to contradiction.

So let’s reconsider.

Maybe “my tenths digit has the lowest value” means it's 0, but that can’t work because then number < 8.5 → rounds to 8.

But clue says it rounds to 9 → so must be ≥8.5 → tenths digit ≥5

So tenths digit cannot be 0 → contradiction.

Therefore, our interpretation of “lowest value” must be wrong.

Alternative idea: “lowest value” might mean it is the smallest digit in the number, not necessarily 0.

But still, if tenths digit is 5 or higher, and it's supposed to be the lowest, then all other digits must be ≥ it.

Let’s suppose tenths digit is 5 → then it's the smallest digit → so all others are ≥5

Let’s try to build the number.

We know:

- Number is < 10, positive → OK
- Three decimal places → XXX.XXX
- Ones digit is even → 0,2,4,6,8
- Rounds to 9 → so number ∈ [8.5, 9.5)
- So ones digit is 8 (since 9 is odd, not allowed)
- So number is 8.xxx
- Since it rounds to 9 → must be ≥8.5 → so tenths digit ≥5
- Let tenths digit = T → T ≥5
- Clue: “My tenths digit has the lowest value” → so T is the smallest digit in the number
- So all other digits ≥ T
- Also: hundredths digit = ones digit = 8 → so hundredths digit = 8
- Thousandths digit = tenths digit + 4

Let’s write:
- Number: 8 . T 8 K
- Where K = T + 4

Now, T ≥5 (from rounding), and K = T+4 → so K ≥9

Digits are 0–9 → so K ≤9 → so K=9 → T+4=9 → T=5

So:
- T = 5
- K = 9
- Number: 8.589

Now check all clues:

1. Positive, less than 10 → ✔
2. Three decimal places → ✔
3. Ones digit is even → 8 → ✔
4. Round to nearest whole number → 8.589 → rounds to 9 → ✔
5. Tenths digit has the lowest value → tenths digit is 5
- Other digits: ones=8, hundredths=8, thousandths=9 → all ≥5 → so yes, 5 is the lowest digit → ✔
6. Hundredths digit = ones digit → 8 = 8 → ✔
7. Thousandths digit = tenths digit + 4 → 9 = 5 + 4 → ✔

Perfect!

So the number is 8.589

Now, do we need all 7 clues?

Let’s see:

- We used:
- Less than 10 → needed
- Three decimal places → needed
- Ones digit even → needed (to eliminate 9)
- Rounds to 9 → needed (to get ≥8.5)
- Tenths digit has lowest value → critical for determining T=5
- Hundredths = ones → key to get 8
- Thousandths = tenths + 4 → gives K = T+4

So all 7 clues were used.

But the question asks: Do you need all 7 of these clues to work out the answer?

Answer: Yes, because without any one of them, ambiguity arises.

For example:
- Without “ones digit even” → could be 9.??? → but 9 is odd → invalid
- Without “rounds to 9” → could be anything
- Without “hundredths = ones” → we wouldn’t know it's 8
- Without “thousandths = tenths + 4” → we couldn’t find K

So yes, all 7 clues are necessary.

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✔ C) Answer: 8.589

And yes, you need all 7 clues.

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✔ Final Answers:

#### A)
1) 0.5
2) 0.8
3) 0.5
4) 0.3
5) 0.07
6) 0.7
7) 0.6
8) 0.3
9) 0.008

#### B)
1) 6.752
2) 0.56
3) 0.02
4) 9.361
5) 0.651
6) 0.014
7) 9.327
8) 5.007
9) 0.308
10) 5.76
11) 7.30
12) 0.07
13) 0.82
14) 1.20
15) 0.390
16) 5.362
17) 0.100
18) 0.201
19) 0.320
20) 0.008

#### C)
The number is 8.589
Yes, you need all 7 clues.

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