Explore · MATH-5B-C09-L05-OPEN
Calculate 0.048 × 10; explain the place-value change.
Great Inheritance Mathematics Term B · Original independent course
Multiply Decimals by 10, 100, and 1,000
Watch for: Moving a printed decimal point without tracking magnitude.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C09-L05-PREREQ
Calculate 4 × 10.
Show worked answer (after attempting)
Answer: 40
Four groups of ten make 40.
Understand the idea
Explain place-value scaling of decimals by powers of ten without digit-loss or zero-append tricks. The essential earlier idea is: 5A powers-of-ten multiplication and Chapter 9 place value.. The model below will always use the actual quantities from the worked problem. Check moving a printed decimal point without tracking magnitude when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C09-L05-Q01
Calculate 0.047 × 10; explain the place-value change.
Solution: 0.47
× 10 changes each digit’s unit by 10. Example 0.047 × 10 = 0.47. This is not an arbitrary add-zero rule.
Worked example 2 · MATH-5B-C09-L05-Q02
A measurement is 3.205 kg. What is 3.205 × 100?
Solution: 320.5 kg
× 100 changes each digit’s unit by 100. Example 3.205 × 100 = 320.5. This is not an arbitrary add-zero rule.
Worked example 3 · MATH-5B-C09-L05-Q03
Estimate, then calculate 0.008 × 1000.
Solution: 8
× 1000 changes each digit’s unit by 1000. Example 0.008 × 1000 = 8. This is not an arbitrary add-zero rule.
Check understanding
1 · MATH-5B-C09-L05-Q04
Calculate 0.048 × 10; explain the place-value change.
Show worked answer (after attempting)
Answer: 0.48
× 10 changes each digit’s unit by 10. Example 0.048 × 10 = 0.48. This is not an arbitrary add-zero rule.
2 · MATH-5B-C09-L05-Q05
A measurement is 3.206 kg. What is 3.206 × 100?
Show worked answer (after attempting)
Answer: 320.6 kg
× 100 changes each digit’s unit by 100. Example 3.206 × 100 = 320.6. This is not an arbitrary add-zero rule.
3 · MATH-5B-C09-L05-Q06
Estimate, then calculate 0.009 × 1000.
Show worked answer (after attempting)
Answer: 9
× 1000 changes each digit’s unit by 1000. Example 0.009 × 1000 = 9. This is not an arbitrary add-zero rule.
Guided practice
1 · MATH-5B-C09-L05-Q07
Calculate 0.049 × 10; explain the place-value change.
Show worked answer (after attempting)
Answer: 0.49
× 10 changes each digit’s unit by 10. Example 0.049 × 10 = 0.49. This is not an arbitrary add-zero rule.
2 · MATH-5B-C09-L05-Q08
A measurement is 3.207 kg. What is 3.207 × 100?
Show worked answer (after attempting)
Answer: 320.7 kg
× 100 changes each digit’s unit by 100. Example 3.207 × 100 = 320.7. This is not an arbitrary add-zero rule.
3 · MATH-5B-C09-L05-Q09
Estimate, then calculate 0.01 × 1000.
Show worked answer (after attempting)
Answer: 10
× 1000 changes each digit’s unit by 1000. Example 0.01 × 1000 = 10. This is not an arbitrary add-zero rule.
4 · MATH-5B-C09-L05-Q10
Calculate 0.05 × 10; explain the place-value change.
Show worked answer (after attempting)
Answer: 0.5
× 10 changes each digit’s unit by 10. Example 0.05 × 10 = 0.5. This is not an arbitrary add-zero rule.
Independent practice
1 · MATH-5B-C09-L05-Q11
A measurement is 3.208 kg. What is 3.208 × 100?
Show worked answer (after attempting)
Answer: 320.8 kg
× 100 changes each digit’s unit by 100. Example 3.208 × 100 = 320.8. This is not an arbitrary add-zero rule.
2 · MATH-5B-C09-L05-Q12
Estimate, then calculate 0.011 × 1000.
Show worked answer (after attempting)
Answer: 11
× 1000 changes each digit’s unit by 1000. Example 0.011 × 1000 = 11. This is not an arbitrary add-zero rule.
3 · MATH-5B-C09-L05-Q13
Calculate 0.051 × 10; explain the place-value change.
Show worked answer (after attempting)
Answer: 0.51
× 10 changes each digit’s unit by 10. Example 0.051 × 10 = 0.51. This is not an arbitrary add-zero rule.
4 · MATH-5B-C09-L05-Q14
A measurement is 3.209 kg. What is 3.209 × 100?
Show worked answer (after attempting)
Answer: 320.9 kg
× 100 changes each digit’s unit by 100. Example 3.209 × 100 = 320.9. This is not an arbitrary add-zero rule.
5 · MATH-5B-C09-L05-Q15
Estimate, then calculate 0.012 × 1000.
Show worked answer (after attempting)
Answer: 12
× 1000 changes each digit’s unit by 1000. Example 0.012 × 1000 = 12. This is not an arbitrary add-zero rule.
6 · MATH-5B-C09-L05-Q16
Calculate 0.052 × 10; explain the place-value change.
Show worked answer (after attempting)
Answer: 0.52
× 10 changes each digit’s unit by 10. Example 0.052 × 10 = 0.52. This is not an arbitrary add-zero rule.
7 · MATH-5B-C09-L05-Q17
A measurement is 3.21 kg. What is 3.21 × 100?
Show worked answer (after attempting)
Answer: 321 kg
× 100 changes each digit’s unit by 100. Example 3.21 × 100 = 321. This is not an arbitrary add-zero rule.
8 · MATH-5B-C09-L05-Q18
Estimate, then calculate 0.013 × 1000.
Show worked answer (after attempting)
Answer: 13
× 1000 changes each digit’s unit by 1000. Example 0.013 × 1000 = 13. This is not an arbitrary add-zero rule.
Challenge and error analysis
1 · MATH-5B-C09-L05-ERR1
The assigned question is: “A measurement is 3.213 kg. What is 3.213 × 100?” A learner wrote: “3.213 × 100 = 321.4. I used this intermediate value to finish the assigned problem.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: 321.3 kg
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 321.3 kg. Recompute from the given data: × 100 changes each digit’s unit by 100. Example 3.213 × 100 = 321.3. This is not an arbitrary add-zero rule.
2 · MATH-5B-C09-L05-ERR2
The assigned question is: “Estimate, then calculate 0.016 × 1000.” A learner wrote: “0.016 × 1000 = 17. I used this intermediate value to finish the assigned problem.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: 16
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 16. Recompute from the given data: × 1000 changes each digit’s unit by 1000. Example 0.016 × 1000 = 16. This is not an arbitrary add-zero rule.
Exit check
Exit · MATH-5B-C09-L05-Q19
Calculate 0.053 × 10; explain the place-value change.
Show worked answer (after attempting)
Answer: 0.53
× 10 changes each digit’s unit by 10. Example 0.053 × 10 = 0.53. This is not an arbitrary add-zero rule.