5th Grade Place Value Worksheets - Free Printable

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

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

We need to identify the place value of the underlined digit.

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

2) 7.832 → ?
- Underlined digit: 8
- It’s in the tenths place → 0.8

3) 23.594 → ?
- Underlined digit: 5
- Tenths place → 0.5

4) 742.391 → ?
- Underlined digit: 3
- Tenths place → 0.3

5) 931.372 → ?
- Underlined digit: 7
- Hundredths place → 0.07

6) 18293.726 → ?
- Underlined digit: 7
- Tenths place → 0.7

7) 26371.659 → ?
- Underlined digit: 6
- Tenths place → 0.6

8) 73298.327 → ?
- Underlined digit: 3
- Tenths place → 0.3

9) 328371.648 → ?
- Underlined digit: 8
- Thousandths place → 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
We have: 8 + 0.3 = 8.3; +0.007 = 8.307 → Need 8.327
So missing: 8.327 − 8.307 = 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
First add 6 + 0.4 = 6.4; then subtract from 6.47: 6.47 − 6.4 = 0.07

13) 8 + _____ + 0.003 = 8.823
First: 8 + 0.003 = 8.003; subtract from 8.823: 8.823 − 8.003 = 0.82

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
Add: 2 + 0.057 = 2.057; subtract from 2.157: 2.157 − 2.057 = 0.100

18) _____ + 6 + 0.04 = 6.241
Add: 6 + 0.04 = 6.04; subtract: 6.241 − 6.04 = 0.201

19) 7.327 = _____ + 7 + 0.007
Add: 7 + 0.007 = 7.007; subtract from 7.327: 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) 0.82
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.

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 analyze step by step.

#### Step 1: Number < 10, 3 decimal places
→ So it's in the form: X.XXX, where X is digit.

#### Step 2: Rounds to 9
→ So the number must be between 8.5 and 9.499..., but since it rounds to 9, it must be ≥ 8.5 and < 9.5

But clue says "I am less than 10", so that fits.

But also, rounding to nearest whole number = 9 → So number is in [8.5, 9.5)

So possible range: 8.5 ≤ number < 9.5

But also, ones digit is even → So the whole number part is even.

Even digits: 0, 2, 4, 6, 8

But number is in [8.5, 9.5), so the ones digit must be 8 or 9?

Wait — if the ones digit is even, and number is at least 8.5, then:

- Ones digit can't be 9 (odd)
- So ones digit must be 8

→ So number is between 8.5 and 8.999...

So number is 8.XXX, with 8.5 ≤ number < 9

Now, rounding to nearest whole number = 9?

But if number is 8.5 to 8.999, it rounds to 9 only if ≥ 8.5 → Yes, that works.

So number is in [8.5, 8.999]

So ones digit = 8 ✔

Also, hundredths digit is the same as ones digit → So hundredths digit = 8

So number is: 8 . _ 8 _

Now, tenths digit has the lowest value → What is the lowest possible digit?

Digits are 0–9, so lowest value is 0

So tenths digit = 0

So now we have: 8 . 0 8 _

Now, thousandths digit is 4 more than tenths digit

Tenths digit = 0 → So thousandths digit = 0 + 4 = 4

So number is: 8.084

Let’s verify all clues:

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

Wait! Problem!

8.084 is less than 8.5, so it rounds to 8, not 9.

But clue says: “If you round me to the nearest whole number, I am 9.”

So number must be ≥ 8.5

But we just got 8.084 → too small.

Contradiction.

So what went wrong?

Ah! Let's recheck.

We said tenths digit has lowest value → we assumed it means smallest possible digit, i.e., 0.

But maybe “lowest value” means something else?

Wait — could it mean the smallest digit in the number?

But the clue says: “My tenths digit has the lowest value.” → likely meaning it is the smallest digit among all digits.

But let’s reconsider.

Wait — perhaps tenths digit is 0, but then number is like 8.0xx → less than 8.5 → rounds to 8, not 9.

But clue says it rounds to 9 → so number must be ≥ 8.5

So tenths digit must be at least 5, because:

- 8.5 → rounds to 9
- 8.4 → rounds to 8

So to round to 9, number ≥ 8.5 → tenths digit ≥ 5

But clue says: “My tenths digit has the lowest value.”

So if tenths digit is ≥ 5, how can it be the “lowest value”?

Unless “lowest value” means numerically smallest, but still, it can’t be both ≥5 and minimal.

Wait — unless we misread.

Let’s list all clues again:

> • 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 suppose tenths digit = 0 → then number is 8.0xx → < 8.5 → rounds to 8 → contradicts clue 4.

So tenths digit cannot be 0.

But clue says “has the lowest value” — maybe it means it is the smallest digit in the number?

Then tenths digit is the smallest digit in the number.

So let’s suppose tenths digit = x, and x is the smallest digit in the number.

We know:

- Ones digit = even → possibilities: 0,2,4,6,8
- But number rounds to 9 → so number ≥ 8.5 → so ones digit must be 8 (since 9 is odd, not allowed)

So ones digit = 8 → so number is 8.XXX

And number ≥ 8.5 → so tenths digit ≥ 5

So tenths digit ∈ {5,6,7,8,9}

Now, hundredths digit = ones digit = 8

So number is: 8 . T 8 K

Where T = tenths digit, K = thousandths digit

Now, K = T + 4

But digits are 0–9, so K ≤ 9 → so T + 4 ≤ 9 → T ≤ 5

But earlier, T ≥ 5 (because number ≥ 8.5)

So T ≥ 5 and T ≤ 5 → T = 5

So tenths digit = 5

Then thousandths digit = 5 + 4 = 9

So number is: 8.589

Now check all clues:

1. Positive number < 10 → yes ✔
2. Three decimal places → yes ✔
3. Ones digit is even → 8 is even ✔
4. Round to nearest whole number → 8.589 → is ≥ 8.5 → rounds to 9 ✔
5. Tenths digit has the lowest value → tenths digit = 5
Digits: 8 (ones), 5 (tenths), 8 (hundredths), 9 (thousandths)
So digits: 8,5,8,9 → smallest is 5 → yes, tenths digit is the smallest → ✔
6. Hundredths digit = ones digit → both 8 → ✔
7. Thousandths digit = 4 more than tenths digit → 9 = 5 + 4 → ✔

All clues satisfied!

✔ Answer: 8.589

Now, the question asks: Do you need all 7 clues?

Let’s see:

- Clue 1: limits to <10 → helpful
- Clue 2: 3dp → needed
- Clue 3: ones digit even → helps narrow to 8
- Clue 4: rounds to 9 → forces ≥8.5 → tenths ≥5
- Clue 5: tenths digit is lowest → key to solving
- Clue 6: hundredths = ones → links digits
- Clue 7: thousandths = tenths + 4 → gives equation

We used all clues. But could we skip any?

For example, without clue 5, we might have multiple options.

Suppose we didn’t know tenths digit was the smallest.

From clues:

- ones digit = 8 (even, and number ≥8.5)
- hundredths digit = 8
- thousandths = tenths + 4
- tenths ≥5, and tenths + 4 ≤9 → tenths ≤5 → so tenths =5
- so thousandths =9
- number = 8.589

So actually, clue 5 is redundant?

Wait — without clue 5, could tenths digit be other values?

No — because:

- tenths ≥5 (from rounding)
- thousandths = tenths + 4 ≤9 → tenths ≤5
→ so tenths =5

So clue 5 is not needed — we deduce tenths=5 from clues 4 and 7.

But clue 5 says tenths digit has lowest value — which is true, but not necessary to find the number.

So do we need all 7 clues?

→ No, we don’t need clue 5 — it’s a consequence.

But it helps confirm.

But the question is: Do you need all 7 to work out the answer?

Answer: No, because clues 4, 6, and 7 force tenths=5, hundredths=8, thousandths=9, ones=8 → 8.589

Clue 5 is extra verification.

But clue 3 ("ones digit is even") is essential — otherwise, could be 9, but 9 is odd.

So yes, we need most, but not all.

But let’s test: if we remove clue 5, can we still get the answer?

Yes — as shown above.

So no, we do not need all 7 clues.

But clue 5 helps ensure consistency.

Final answer: The number is 8.589, and you do not need all 7 clues — you can deduce it from others.

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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)
- Who am I? → 8.589
- Do you need all 7 clues? → No, you don’t need all 7 — clue 5 is redundant.

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