Place Value to 3DP Worksheet 6: Practice decimal place value, missing numbers, and solve a riddle with a salamander theme.

Let's solve this step-by-step, working through each section of the worksheet.

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

We need to identify the value of the underlined digit — that is, what it represents in terms of place value (e.g., tenths, hundredths, thousandths).

1) 34.526 → 0.5
- Underlined digit: 5
- It's in the tenths place → value = 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

✔ Answers for 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

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B) Fill in the missing numbers.

We’ll go through each one:

1) 6 + 0.7 + 0.05 + 0.002 = ?
Add: 6 + 0.7 = 6.7; +0.05 = 6.75; +0.002 = 6.752

2) 7 + ____ = 7.56
Subtract: 7.56 - 7 = 0.56

3) 8.327 = 8 + 0.3 + ____ + 0.007
Break down: 8.327 = 8 + 0.3 + 0.02 + 0.007 → So missing = 0.02

4) ____ = 9 + 0.3 + 0.06 + 0.001
Add: 9 + 0.3 = 9.3; +0.06 = 9.36; +0.001 = 9.361

5) 8 + ____ = 8.651
Subtract: 8.651 - 8 = 0.651

6) 7.5 + ____ = 7.514
Subtract: 7.514 - 7.5 = 0.014

7) 9 + 0.327 = ____
Add: 9 + 0.327 = 9.327

8) ____ = 5 + 0.007
Add: 5 + 0.007 = 5.007

9) 0.3 + 0.008 = ____
Add: 0.3 + 0.008 = 0.308

10) 0.7 + 0.06 + 5 = ____
Add: 0.7 + 0.06 = 0.76; +5 = 5.76

11) 7.34 = 0.04 + ____
Subtract: 7.34 - 0.04 = 7.30

12) ____ + 6 + 0.4 = 6.47
Total of known: 6 + 0.4 = 6.4
So: 6.47 - 6.4 = 0.07

13) 8 + ____ + 0.003 = 8.823
Known: 8 + 0.003 = 8.003
So: 8.823 - 8.003 = 0.820

14) 0.09 + ____ = 1.29
Subtract: 1.29 - 0.09 = 1.20

15) 6.392 = 6.002 + ____
Subtract: 6.392 - 6.002 = 0.390

16) ____ = 5 + 0.002 + 0.36
Add: 5 + 0.002 = 5.002; +0.36 = 5.362

17) 2 + 0.057 + ____ = 2.157
Known: 2 + 0.057 = 2.057
Subtract: 2.157 - 2.057 = 0.100

18) ____ + 6 + 0.04 = 6.241
Known: 6 + 0.04 = 6.04
Subtract: 6.241 - 6.04 = 0.201

19) 7.327 = ____ + 7 + 0.007
Known: 7 + 0.007 = 7.007
Subtract: 7.327 - 7.007 = 0.320

20) 6.24 + ____ = 6.248
Subtract: 6.248 - 6.24 = 0.008

✔ Answers for 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) 0.820
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.

Clues:
- I am a positive number less than 10.
- I have three decimal places.
- My ones digit is an even number.
- If you round me to the nearest whole number, I am 9.
- My tenths digit has the lowest value.
- My hundredths digit is the same as my ones digit.
- My thousandths digit is 4 more than my tenths digit.

Let’s work through this logically.

Let the number be: X.YZW, where:
- X = ones digit
- Y = tenths
- Z = hundredths
- W = thousandths

#### Step 1: “I am a positive number less than 10.”
So, X is from 1 to 9.

#### Step 2: “I have three decimal places.”
So it’s like 5.123 or 9.876 — yes, already assumed.

#### Step 3: “My ones digit is an even number.”
So X ∈ {2, 4, 6, 8} (since it must be even)

#### Step 4: “If you round me to the nearest whole number, I am 9.”
This means the number is between 8.5 and 9.5, but since it rounds to 9, it must be ≥ 8.5 and < 9.5.

But also, since the ones digit is even, and the number rounds to 9, the ones digit must be 8.

Why? Because if it were 6 or 4, then even with high decimals, it would round to 6 or 7 or 8, not 9.

For example:
- 8.5 → rounds to 9
- 8.999 → rounds to 9
- But 6.999 → rounds to 7
- 4.999 → rounds to 5

So only possible even ones digit that can round to 9 is 8.

So: X = 8

Now we know: 8.YZW

And it rounds to 9 → so the number must be ≥ 8.5

So: 8.YZW ≥ 8.5 → so Y (tenths digit) must be at least 5.

But next clue:

#### Step 5: “My tenths digit has the lowest value.”

"Lowest value" likely means the smallest possible digit (i.e., 0), but wait — if tenths digit is 0, then number is 8.0?? → which is less than 8.5 → won’t round to 9.

But earlier we said it must be ≥ 8.5 → so tenths digit must be at least 5.

So how can the tenths digit have the "lowest value"?

Possibility: “lowest value” means minimum possible value given constraints.

But the tenths digit must be ≥ 5 to round up to 9.

So the lowest possible value it can have is 5.

So tenths digit = 5

→ Y = 5

So now: 8.5ZW

#### Step 6: “My hundredths digit is the same as my ones digit.”

Ones digit = 8 → so Z = 8

→ Now: 8.58W

#### Step 7: “My thousandths digit is 4 more than my tenths digit.”

Tenths digit = 5 → so W = 5 + 4 = 9

So W = 9

Final number: 8.589

Now check all clues:

- Positive number less than 10? → Yes (8.589)
- Three decimal places? → Yes
- Ones digit even? → 8 → yes
- Rounds to nearest whole number → 8.589 → rounds to 9 → yes
- Tenths digit has the lowest value? → Tenths digit is 5. Is this the lowest possible? Given rounding to 9, yes — 5 is the smallest tenths digit possible to round up to 9. So “lowest value” here likely means smallest possible value under constraints → acceptable.
- Hundredths digit = ones digit? → 8 = 8 → yes
- Thousandths digit = 4 more than tenths digit? → 5 + 4 = 9 → yes

✔ All clues satisfied!

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✔ Final Answer for C): 8.589

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

Let’s see:
We used:
- Clue 1: limits range
- Clue 2: format
- Clue 3: restricts ones digit
- Clue 4: forces ones digit to be 8
- Clue 5: forces tenths digit to be 5 (lowest possible to round to 9)
- Clue 6: gives Z = 8
- Clue 7: gives W = 9

But could we skip any?

Suppose we didn't have clue 5 ("tenths digit has lowest value") — could we still get it?

Well, tenths digit must be ≥ 5 to round to 9.

But if it were 6, 7, 8, or 9, then the number would be higher.

But clue 7 says: thousandths digit = tenths digit + 4

Since digits go from 0–9, tenths digit + 4 ≤ 9 → so tenths digit ≤ 5

So tenths digit ≤ 5 and ≥ 5 → must be exactly 5

So clue 5 is redundant — we can deduce tenths digit = 5 from clue 7 and the rounding constraint.

Similarly, clue 6 and 7 give us Z and W directly.

So no, we do not need all 7 clues.

We can deduce the number using just:
- Clue 1, 2, 3, 4, 6, 7 → and clue 5 is extra.

Or even without clue 5, we can deduce tenths digit = 5 from clue 7 and rounding.

So: No, we don’t need all 7 clues.

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✔ Final Answers Summary:

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A) Place Value:

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) Missing Numbers:

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) 0.820
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) Who am I?

Answer: 8.589
Do you need all 7 clues? No — clue 5 is redundant.

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✔ All done!