Students can use this sheet to practice converting expanded decimal notation into standard form and finding missing values.
Place value to 3 decimal places math worksheet sheet 5a with expanded form questions.
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Step-by-step solution for: Place Value. Mathematics Worksheets and Study Guides Fifth Grade.
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Show Answer Key & Explanations
Step-by-step solution for: Place Value. Mathematics Worksheets and Study Guides Fifth Grade.
Let's solve each problem on "Place Value to 3DP Sheet 5A" step by step. The goal is to understand place value up to three decimal places (thousandths). We'll go through all 40 problems, filling in the blanks and explaining key concepts.
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- Units (ones): whole number part
- Tenths: first digit after decimal → ×0.1
- Hundredths: second digit after decimal → ×0.01
- Thousandths: third digit after decimal → ×0.001
So:
> 6.352 = 6 + 0.3 + 0.05 + 0.002
> = 6 (units) + 3 tenths + 5 hundredths + 2 thousandths
---
Now let’s solve each one:
---
1) 6 + 0.3 + 0.05 + 0.002 = 6.352
✔️ Already given. Correct.
2) 8 + 0.2 + 0.08 + 0.001 = ?
= 8 + 0.2 = 8.2
+ 0.08 = 8.28
+ 0.001 = 8.281
✔ Answer: 8.281
3) 2 + 0.7 + 0.03 + 0.005 = ?
= 2 + 0.7 = 2.7
+ 0.03 = 2.73
+ 0.005 = 2.735
✔ Answer: 2.735
4) 4 + 0.3 + 0.01 + 0.008 = ?
= 4 + 0.3 = 4.3
+ 0.01 = 4.31
+ 0.008 = 4.318
✔ Answer: 4.318
5) ______ = 9 + 0.5 + 0.09
= 9 + 0.5 = 9.5
+ 0.09 = 9.59
✔ Answer: 9.59
6) 0.3 + 0.02 + 0.008 = ?
= 0.3 + 0.02 = 0.32
+ 0.008 = 0.328
✔ Answer: 0.328
7) ______ = 4 + 0.05 + 0.006
= 4 + 0.05 = 4.05
+ 0.006 = 4.056
✔ Answer: 4.056
8) 6 + 0.7 + 0.001 = ?
= 6 + 0.7 = 6.7
+ 0.001 = 6.701
✔ Answer: 6.701
9) 0.3 + 0.008 = ?
= 0.300 + 0.008 = 0.308
✔ Answer: 0.308
10) 5 + 0.3 + 0.06 + 0.003 = ?
= 5 + 0.3 = 5.3
+ 0.06 = 5.36
+ 0.003 = 5.363
✔ Answer: 5.363
11) ______ = 6 + 0.4 + 0.002
= 6 + 0.4 = 6.4
+ 0.002 = 6.402
✔ Answer: 6.402
12) 0.08 + 0.005 = ?
= 0.085
✔ Answer: 0.085
13) 12 + 0.7 + 0.004 = ?
= 12 + 0.7 = 12.7
+ 0.004 = 12.704
✔ Answer: 12.704
14) 15 + 0.36 = ?
= 15.36
✔ Answer: 15.36
15) ______ = 30 + 2 + 0.304
= 30 + 2 = 32
+ 0.304 = 32.304
✔ Answer: 32.304
16) 80 + 0.2 + 0.06 + 0.007 = ?
= 80 + 0.2 = 80.2
+ 0.06 = 80.26
+ 0.007 = 80.267
✔ Answer: 80.267
17) 1 + 0.084 = ?
= 1.084
✔ Answer: 1.084
18) 25 + 0.3 + 0.06 + 0.001 = ?
= 25 + 0.3 = 25.3
+ 0.06 = 25.36
+ 0.001 = 25.361
✔ Answer: 25.361
19) ______ = 7 + 0.05 + 0.002
= 7 + 0.05 = 7.05
+ 0.002 = 7.052
✔ Answer: 7.052
20) 9 + 0.006 = ?
= 9.006
✔ Answer: 9.006
---
21) 6 + 0.4 + ____ + 0.003 = 6.423
We know:
6 + 0.4 = 6.4
6.4 + 0.003 = 6.403
But total should be 6.423 → missing 6.423 – 6.403 = 0.02
So blank = 0.02
✔ Answer: 0.02
22) 2 + ____ + 0.05 + 0.007 = 2.657
2 + 0.05 = 2.05
+ 0.007 = 2.057
Total needed: 2.657 → difference = 2.657 – 2.057 = 0.6
So blank = 0.6
✔ Answer: 0.6
23) 7.284 = 7 + 0.2 + 0.08 + ____
7 + 0.2 = 7.2
+ 0.08 = 7.28
Need 7.284 → so missing 0.004
✔ Answer: 0.004
24) ____ + 0.3 + 0.05 + 0.001 = 9.351
0.3 + 0.05 = 0.35
+ 0.001 = 0.351
Total = 9.351 → so missing = 9.351 – 0.351 = 9
✔ Answer: 9
25) 7.28 = 7 + ____
7.28 – 7 = 0.28
✔ Answer: 0.28
26) 1 + ____ = 1.325
1.325 – 1 = 0.325
✔ Answer: 0.325
27) 8.39 = 8 + ____ + 0.09
8 + 0.09 = 8.09
8.39 – 8.09 = 0.3
✔ Answer: 0.3
28) 4 + ____ + 0.002 = 4.032
4 + 0.002 = 4.002
4.032 – 4.002 = 0.03
✔ Answer: 0.03
29) 9.036 = 9 + ____
9.036 – 9 = 0.036
✔ Answer: 0.036
30) 3 + ____ + 0.002 = 3.702
3 + 0.002 = 3.002
3.702 – 3.002 = 0.7
✔ Answer: 0.7
31) 7.32 = 7 + 0.3 + ____
7 + 0.3 = 7.3
7.32 – 7.3 = 0.02
✔ Answer: 0.02
32) 6 + 0.1 + ____ = 6.104
6 + 0.1 = 6.1
6.104 – 6.1 = 0.004
✔ Answer: 0.004
33) 5.237 = 5 + ____
5.237 – 5 = 0.237
✔ Answer: 0.237
34) 4.129 = 4 + 0.1 + ____ + 0.009
4 + 0.1 = 4.1
+ 0.009 = 4.109
4.129 – 4.109 = 0.02
✔ Answer: 0.02
35) ____ + 0.062 = 7.362
7.362 – 0.062 = 7.3
✔ Answer: 7.3
36) ____ + 0.005 = 0.325
0.325 – 0.005 = 0.32
✔ Answer: 0.32
37) 0.716 = ____ + 0.006
0.716 – 0.006 = 0.71
✔ Answer: 0.71
38) 1.83 = ____ + 1
1.83 – 1 = 0.83
✔ Answer: 0.83
39) 2.536 = 2.5 + ____
2.536 – 2.5 = 0.036
✔ Answer: 0.036
40) 9.7 + ____ = 9.728
9.728 – 9.7 = 0.028
✔ Answer: 0.028
---
| Problem | Answer |
|--------|--------|
| 1 | 6.352 |
| 2 | 8.281 |
| 3 | 2.735 |
| 4 | 4.318 |
| 5 | 9.59 |
| 6 | 0.328 |
| 7 | 4.056 |
| 8 | 6.701 |
| 9 | 0.308 |
|10 | 5.363 |
|11 | 6.402 |
|12 | 0.085 |
|13 | 12.704 |
|14 | 15.36 |
|15 | 32.304 |
|16 | 80.267 |
|17 | 1.084 |
|18 | 25.361 |
|19 | 7.052 |
|20 | 9.006 |
|21 | 0.02 |
|22 | 0.6 |
|23 | 0.004 |
|24 | 9 |
|25 | 0.28 |
|26 | 0.325 |
|27 | 0.3 |
|28 | 0.03 |
|29 | 0.036 |
|30 | 0.7 |
|31 | 0.02 |
|32 | 0.004 |
|33 | 0.237 |
|34 | 0.02 |
|35 | 7.3 |
|36 | 0.32 |
|37 | 0.71 |
|38 | 0.83 |
|39 | 0.036 |
|40 | 0.028 |
---
- Always align decimals when adding.
- Think of each place: units, tenths, hundredths, thousandths.
- When breaking down numbers, write them as sum of parts (e.g., 3.456 = 3 + 0.4 + 0.05 + 0.006).
- Use subtraction to find missing values: total – known parts = missing part.
Let me know if you'd like a printable version or explanation of any specific problem!
---
🔢 Understanding Place Value:
- Units (ones): whole number part
- Tenths: first digit after decimal → ×0.1
- Hundredths: second digit after decimal → ×0.01
- Thousandths: third digit after decimal → ×0.001
So:
> 6.352 = 6 + 0.3 + 0.05 + 0.002
> = 6 (units) + 3 tenths + 5 hundredths + 2 thousandths
---
Now let’s solve each one:
---
✔ Problems 1–20
1) 6 + 0.3 + 0.05 + 0.002 = 6.352
✔️ Already given. Correct.
2) 8 + 0.2 + 0.08 + 0.001 = ?
= 8 + 0.2 = 8.2
+ 0.08 = 8.28
+ 0.001 = 8.281
✔ Answer: 8.281
3) 2 + 0.7 + 0.03 + 0.005 = ?
= 2 + 0.7 = 2.7
+ 0.03 = 2.73
+ 0.005 = 2.735
✔ Answer: 2.735
4) 4 + 0.3 + 0.01 + 0.008 = ?
= 4 + 0.3 = 4.3
+ 0.01 = 4.31
+ 0.008 = 4.318
✔ Answer: 4.318
5) ______ = 9 + 0.5 + 0.09
= 9 + 0.5 = 9.5
+ 0.09 = 9.59
✔ Answer: 9.59
6) 0.3 + 0.02 + 0.008 = ?
= 0.3 + 0.02 = 0.32
+ 0.008 = 0.328
✔ Answer: 0.328
7) ______ = 4 + 0.05 + 0.006
= 4 + 0.05 = 4.05
+ 0.006 = 4.056
✔ Answer: 4.056
8) 6 + 0.7 + 0.001 = ?
= 6 + 0.7 = 6.7
+ 0.001 = 6.701
✔ Answer: 6.701
9) 0.3 + 0.008 = ?
= 0.300 + 0.008 = 0.308
✔ Answer: 0.308
10) 5 + 0.3 + 0.06 + 0.003 = ?
= 5 + 0.3 = 5.3
+ 0.06 = 5.36
+ 0.003 = 5.363
✔ Answer: 5.363
11) ______ = 6 + 0.4 + 0.002
= 6 + 0.4 = 6.4
+ 0.002 = 6.402
✔ Answer: 6.402
12) 0.08 + 0.005 = ?
= 0.085
✔ Answer: 0.085
13) 12 + 0.7 + 0.004 = ?
= 12 + 0.7 = 12.7
+ 0.004 = 12.704
✔ Answer: 12.704
14) 15 + 0.36 = ?
= 15.36
✔ Answer: 15.36
15) ______ = 30 + 2 + 0.304
= 30 + 2 = 32
+ 0.304 = 32.304
✔ Answer: 32.304
16) 80 + 0.2 + 0.06 + 0.007 = ?
= 80 + 0.2 = 80.2
+ 0.06 = 80.26
+ 0.007 = 80.267
✔ Answer: 80.267
17) 1 + 0.084 = ?
= 1.084
✔ Answer: 1.084
18) 25 + 0.3 + 0.06 + 0.001 = ?
= 25 + 0.3 = 25.3
+ 0.06 = 25.36
+ 0.001 = 25.361
✔ Answer: 25.361
19) ______ = 7 + 0.05 + 0.002
= 7 + 0.05 = 7.05
+ 0.002 = 7.052
✔ Answer: 7.052
20) 9 + 0.006 = ?
= 9.006
✔ Answer: 9.006
---
✔ Problems 21–40
21) 6 + 0.4 + ____ + 0.003 = 6.423
We know:
6 + 0.4 = 6.4
6.4 + 0.003 = 6.403
But total should be 6.423 → missing 6.423 – 6.403 = 0.02
So blank = 0.02
✔ Answer: 0.02
22) 2 + ____ + 0.05 + 0.007 = 2.657
2 + 0.05 = 2.05
+ 0.007 = 2.057
Total needed: 2.657 → difference = 2.657 – 2.057 = 0.6
So blank = 0.6
✔ Answer: 0.6
23) 7.284 = 7 + 0.2 + 0.08 + ____
7 + 0.2 = 7.2
+ 0.08 = 7.28
Need 7.284 → so missing 0.004
✔ Answer: 0.004
24) ____ + 0.3 + 0.05 + 0.001 = 9.351
0.3 + 0.05 = 0.35
+ 0.001 = 0.351
Total = 9.351 → so missing = 9.351 – 0.351 = 9
✔ Answer: 9
25) 7.28 = 7 + ____
7.28 – 7 = 0.28
✔ Answer: 0.28
26) 1 + ____ = 1.325
1.325 – 1 = 0.325
✔ Answer: 0.325
27) 8.39 = 8 + ____ + 0.09
8 + 0.09 = 8.09
8.39 – 8.09 = 0.3
✔ Answer: 0.3
28) 4 + ____ + 0.002 = 4.032
4 + 0.002 = 4.002
4.032 – 4.002 = 0.03
✔ Answer: 0.03
29) 9.036 = 9 + ____
9.036 – 9 = 0.036
✔ Answer: 0.036
30) 3 + ____ + 0.002 = 3.702
3 + 0.002 = 3.002
3.702 – 3.002 = 0.7
✔ Answer: 0.7
31) 7.32 = 7 + 0.3 + ____
7 + 0.3 = 7.3
7.32 – 7.3 = 0.02
✔ Answer: 0.02
32) 6 + 0.1 + ____ = 6.104
6 + 0.1 = 6.1
6.104 – 6.1 = 0.004
✔ Answer: 0.004
33) 5.237 = 5 + ____
5.237 – 5 = 0.237
✔ Answer: 0.237
34) 4.129 = 4 + 0.1 + ____ + 0.009
4 + 0.1 = 4.1
+ 0.009 = 4.109
4.129 – 4.109 = 0.02
✔ Answer: 0.02
35) ____ + 0.062 = 7.362
7.362 – 0.062 = 7.3
✔ Answer: 7.3
36) ____ + 0.005 = 0.325
0.325 – 0.005 = 0.32
✔ Answer: 0.32
37) 0.716 = ____ + 0.006
0.716 – 0.006 = 0.71
✔ Answer: 0.71
38) 1.83 = ____ + 1
1.83 – 1 = 0.83
✔ Answer: 0.83
39) 2.536 = 2.5 + ____
2.536 – 2.5 = 0.036
✔ Answer: 0.036
40) 9.7 + ____ = 9.728
9.728 – 9.7 = 0.028
✔ Answer: 0.028
---
✔ Final Answers Summary:
| Problem | Answer |
|--------|--------|
| 1 | 6.352 |
| 2 | 8.281 |
| 3 | 2.735 |
| 4 | 4.318 |
| 5 | 9.59 |
| 6 | 0.328 |
| 7 | 4.056 |
| 8 | 6.701 |
| 9 | 0.308 |
|10 | 5.363 |
|11 | 6.402 |
|12 | 0.085 |
|13 | 12.704 |
|14 | 15.36 |
|15 | 32.304 |
|16 | 80.267 |
|17 | 1.084 |
|18 | 25.361 |
|19 | 7.052 |
|20 | 9.006 |
|21 | 0.02 |
|22 | 0.6 |
|23 | 0.004 |
|24 | 9 |
|25 | 0.28 |
|26 | 0.325 |
|27 | 0.3 |
|28 | 0.03 |
|29 | 0.036 |
|30 | 0.7 |
|31 | 0.02 |
|32 | 0.004 |
|33 | 0.237 |
|34 | 0.02 |
|35 | 7.3 |
|36 | 0.32 |
|37 | 0.71 |
|38 | 0.83 |
|39 | 0.036 |
|40 | 0.028 |
---
📌 Tips for Understanding:
- Always align decimals when adding.
- Think of each place: units, tenths, hundredths, thousandths.
- When breaking down numbers, write them as sum of parts (e.g., 3.456 = 3 + 0.4 + 0.05 + 0.006).
- Use subtraction to find missing values: total – known parts = missing part.
Let me know if you'd like a printable version or explanation of any specific problem!
Parent Tip: Review the logic above to help your child master the concept of place value 5th grade math.
