5th Grade Place Value Worksheets - Free Printable

Problem Analysis and Solution

The worksheet provided focuses on place value and decimal arithmetic. Let's solve each section step by step.

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

#### Instructions:
For each number, identify the value of the underlined digit based on its place value.

#### Solutions:
1. 34.526 → 0.5
- The underlined digit is 5, which is in the tenths place.
- Value: 0.5

2. 7.832 →
- The underlined digit is 8, which is in the tenths place.
- Value: 0.8

3. 23.594 →
- The underlined digit is 5, which is in the tenths place.
- Value: 0.5

4. 742.391 →
- The underlined digit is 3, which is in the tenths place.
- Value: 0.3

5. 931.372 →
- The underlined digit is 7, which is in the hundredths place.
- Value: 0.07

6. 18293.726 →
- The underlined digit is 7, which is in the tenths place.
- Value: 0.7

7. 26371.659 →
- The underlined digit is 9, which is in the thousandths place.
- Value: 0.009

8. 73298.327 →
- The underlined digit is 7, which is in the thousandths place.
- Value: 0.007

9. 328371.648 →
- The underlined digit is 8, which is in the thousandths place.
- Value: 0.008

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Section B: Fill in the missing numbers.

#### Instructions:
Complete the equations by filling in the missing numbers.

#### Solutions:

1. 6 + 0.7 + 0.05 + 0.002 = ______
- Sum: \( 6 + 0.7 + 0.05 + 0.002 = 6.752 \)
- Answer: 6.752

2. 7 + ______ = 7.56
- Missing number: \( 7.56 - 7 = 0.56 \)
- Answer: 0.56

3. 8.327 = 8 + 0.3 + ______ + 0.007
- Rearrange: \( 8.327 - 8 - 0.3 - 0.007 = 0.02 \)
- Answer: 0.02

4. _______ = 9 + 0.3 + 0.06 + 0.001
- Sum: \( 9 + 0.3 + 0.06 + 0.001 = 9.361 \)
- Answer: 9.361

5. 8 + ______ = 8.651
- Missing number: \( 8.651 - 8 = 0.651 \)
- Answer: 0.651

6. 7.5 + ______ = 7.514
- Missing number: \( 7.514 - 7.5 = 0.014 \)
- Answer: 0.014

7. 9 + 0.327 = ______
- Sum: \( 9 + 0.327 = 9.327 \)
- Answer: 9.327

8. _______ = 5 + 0.007
- Sum: \( 5 + 0.007 = 5.007 \)
- Answer: 5.007

9. 0.3 + 0.008 = ______
- Sum: \( 0.3 + 0.008 = 0.308 \)
- Answer: 0.308

10. 0.7 + 0.06 + 5 = ______
- Sum: \( 0.7 + 0.06 + 5 = 5.76 \)
- Answer: 5.76

11. 7.34 = 0.04 + ______
- Missing number: \( 7.34 - 0.04 = 7.3 \)
- Answer: 7.3

12. ______ + 6 + 0.4 = 6.47
- Missing number: \( 6.47 - 6 - 0.4 = 0.07 \)
- Answer: 0.07

13. 8 + ______ + 0.003 = 8.823
- Missing number: \( 8.823 - 8 - 0.003 = 0.82 \)
- Answer: 0.82

14. 0.09 + ______ = 1.29
- Missing number: \( 1.29 - 0.09 = 1.2 \)
- Answer: 1.2

15. 6.392 = 6.002 + ______
- Missing number: \( 6.392 - 6.002 = 0.39 \)
- Answer: 0.39

16. ______ = 5 + 0.002 + 0.36
- Sum: \( 5 + 0.002 + 0.36 = 5.362 \)
- Answer: 5.362

17. 2 + 0.057 + ______ = 2.157
- Missing number: \( 2.157 - 2 - 0.057 = 0.1 \)
- Answer: 0.1

18. ______ + 6 + 0.04 = 6.241
- Missing number: \( 6.241 - 6 - 0.04 = 0.201 \)
- Answer: 0.201

19. 7.327 = ______ + 7 + 0.007
- Missing number: \( 7.327 - 7 - 0.007 = 0.32 \)
- Answer: 0.32

20. 6.24 + ______ = 6.248
- Missing number: \( 6.248 - 6.24 = 0.008 \)
- Answer: 0.008

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Section C: Work out the answer from the clues.

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

#### Step-by-Step Reasoning:

1. Clue 1: The number is positive and less than 10.
- Range: \( 0 \leq \text{number} < 10 \).

2. Clue 2: The number has three decimal places.
- Format: \( x.yzw \) (where \( x \) is the ones digit, \( y \) is the tenths digit, \( z \) is the hundredths digit, and \( w \) is the thousandths digit).

3. Clue 3: The ones digit is an even number.
- Possible ones digits: \( 0, 2, 4, 6, 8 \).

4. Clue 4: Rounding to the nearest whole number gives 9.
- This means the number is between 8.5 and 9.499... (inclusive of 8.5 but exclusive of 9.5).

5. Clue 5: The tenths digit has the lowest value.
- Lowest value for a digit is 0.
- Tenths digit \( y = 0 \).

6. Clue 6: The hundredths digit is the same as the ones digit.
- Let the ones digit be \( x \). Then the hundredths digit \( z = x \).

7. Clue 7: The thousandths digit is 4 more than the tenths digit.
- Tenths digit \( y = 0 \).
- Thousandths digit \( w = 0 + 4 = 4 \).

#### Combining the Clues:
- From Clue 4, the number is between 8.5 and 9.499...
- From Clue 3, the ones digit \( x \) is even.
- From Clue 5, the tenths digit \( y = 0 \).
- From Clue 6, the hundredths digit \( z = x \).
- From Clue 7, the thousandths digit \( w = 4 \).

Thus, the number is in the form \( 9.x04 \), where \( x \) is an even digit. Since the number must round to 9, \( x \) can only be 8 (as 9.804 rounds to 9).

#### Final Number:
- Ones digit \( x = 8 \)
- Tenths digit \( y = 0 \)
- Hundredths digit \( z = 8 \)
- Thousandths digit \( w = 4 \)

The number is: 9.804.

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Final Answers:

Section A:
1. 0.5
2. 0.8
3. 0.5
4. 0.3
5. 0.07
6. 0.7
7. 0.009
8. 0.007
9. 0.008

Section 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. 7.3
12. 0.07
13. 0.82
14. 1.2
15. 0.39
16. 5.362
17. 0.1
18. 0.201
19. 0.32
20. 0.008

Section C:
The number is: \boxed{9.804}