Math worksheet focusing on decimal place value, featuring exercises to identify underlined digits, fill in missing numbers, and solve a riddle about a number with specific decimal properties.

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

---

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

We need to identify the value (not just the digit) of the underlined digit based on 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
- It's in the 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

---

B) Fill in the missing numbers.

We’ll go one by one:

1) 6 + 0.7 + 0.05 + 0.002 = ?
→ 6 + 0.7 = 6.7; +0.05 = 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; +0.007 = 8.307 → so missing part = 8.327 – 8.307 = 0.02

4) ___ = 9 + 0.3 + 0.06 + 0.001
→ 9 + 0.3 = 9.3; +0.06 = 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; +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; +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

---

✔ 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) 0.82
14) 1.20
15) 0.390
16) 5.362
17) 0.100
18) 0.201
19) 0.320
20) 0.008

---

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 break it down.

#### Step 1: Number format
- Three decimal places → form: `X.XXX`
- Less than 10 → ones digit ≤ 9
- Rounded to nearest whole number is 9 → must be between 8.5 and 9.499...

So the number is in the range: 8.5 ≤ x < 9.5

But since it rounds to 9, it must be ≥ 8.5 and < 9.5.

Also, ones digit is even → possible ones digits: 0, 2, 4, 6, 8

But since the number is between 8.5 and 9.5, the ones digit must be 8 (because if it were 9, it would be ≥9, but we’re less than 10, and rounding to 9 suggests it's not quite 9.5 or above).

Wait — could it be 8.xxx?

Yes! Because:
- If the number is 8.5 or above, it rounds up to 9.
- But if it's 8.499, it rounds down to 8 → so must be ≥ 8.5

So: 8.5 ≤ x < 9.5

And ones digit is even → only possibility is 8

So the number is 8.XXX

Now:
- Ones digit = 8 → even ✔
- Number is between 8.5 and 9.5 → rounds to 9 ✔

Now:
- Tenths digit has the lowest value → lowest possible digit is 0 → so tenths digit = 0

But wait: the number is at least 8.5 → so tenths digit must be ≥ 5!

Contradiction?

Wait — let’s check.

If the number is 8.5 or higher, then tenths digit is at least 5.

But clue says: "My tenths digit has the lowest value" → what does that mean?

Possibly: among all digits, the tenths digit is the smallest.

But let's see:

We know:
- Ones digit = 8
- Number ≥ 8.5 → tenths digit ≥ 5
- So tenths digit is at least 5 → can’t be 0

So “lowest value” probably means it's the smallest digit in the number, not necessarily 0.

So tenths digit is some digit, and it's the smallest among all digits.

Let’s suppose:
- Ones digit = 8
- Tenths digit = T
- Hundredths digit = H
- Thousandths digit = K

We know:
1. Number ≥ 8.5 → T ≥ 5
2. T is the lowest digit in the number → so T ≤ H and T ≤ K and T ≤ 8
3. H = ones digit = 8 → so hundredths digit = 8
4. K = T + 4 → thousandths digit is 4 more than tenths digit

So:
- H = 8
- K = T + 4
- T ≥ 5 (from ≥ 8.5)
- T ≤ H = 8 → so T ≤ 8
- Also, T ≤ K → but K = T + 4 → so T ≤ T + 4 → always true
- And T must be ≤ H (8) and ≤ K (T+4) → okay
- But also, T must be ≤ all other digits: ones=8, H=8, K=T+4

So T must be ≤ 8, and T ≤ K = T+4 → fine.

But T must be the smallest digit in the number.

Digits: 8 (ones), T (tenths), 8 (hundredths), K = T+4 (thousandths)

So T must be ≤ 8, ≤ 8, ≤ (T+4) → okay

But T must be less than or equal to all others, and since 8 is already there, and T ≥ 5, T cannot be smaller than 5.

But is T the smallest? Only if T ≤ 8 and T ≤ (T+4) → yes, but T+4 > T, so T is smaller than K.

But is T smaller than 8? Only if T < 8 → so T ≤ 7

But T ≥ 5 → so T = 5, 6, or 7

Now, K = T + 4 → so:
- If T = 5 → K = 9 → digits: 8, 5, 8, 9 → smallest is 5 → T is smallest ✔
- If T = 6 → K = 10 → invalid (digit can't be 10)
- If T = 7 → K = 11 → invalid

So only possible: T = 5, K = 9

Then:
- Number = 8.589

Check all clues:

1. Positive number less than 10 → 8.589 ✔
2. Three decimal places → 8.589 ✔
3. Ones digit is even → 8 is even ✔
4. Round to nearest whole number → 8.589 → rounds to 9 ✔
5. Tenths digit has the lowest value → tenths digit = 5
Digits: 8 (ones), 5 (tenths), 8 (hundredths), 9 (thousandths) → smallest is 5 → ✔
6. Hundredths digit is same as ones digit → 8 = 8 ✔
7. Thousandths digit is 4 more than tenths digit → 5 + 4 = 9 → ✔

All clues satisfied!

---

✔ Answer for C): 8.589

---

✔ 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)
8.589

> 💡 Note: You don’t need all 7 clues — the key ones are:
> - Rounds to 9 → so ≥ 8.5
> - Ones digit even → 8
> - Hundredths digit = ones digit → 8
> - Thousandths = tenths + 4
> - Tenths is smallest digit
> These narrow it down uniquely.

Let me know if you'd like a printable version or explanation in simpler terms!