Explore · MATH-5B-C09-L06-OPEN
Calculate 0.048 ÷ 10; explain the place-value change.
Great Inheritance Mathematics Term B · Original independent course
Divide Decimals by 10, 100, and 1,000
Watch for: Writing 0.043 as 0.43 when dividing by 100.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C09-L06-PREREQ
Calculate 400 ÷ 10.
Show worked answer (after attempting)
Answer: 40
Ten groups of 40 make 400.
Understand the idea
Use exchanges of decimal units to divide by powers of ten and verify quotient magnitude. The essential earlier idea is: 5A division by powers of ten and decimal scaling.. The model below will always use the actual quantities from the worked problem. Check writing 0.043 as 0.43 when dividing by 100 when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C09-L06-Q01
Calculate 0.047 ÷ 10; explain the place-value change.
Solution: 0.0047
÷ 10 changes each digit’s unit by 10. Example 0.047 ÷ 10 = 0.0047. This is not an arbitrary add-zero rule.
Worked example 2 · MATH-5B-C09-L06-Q02
A measurement is 3.205 kg. What is 3.205 ÷ 100?
Solution: 0.03205 kg
÷ 100 changes each digit’s unit by 100. Example 3.205 ÷ 100 = 0.03205. This is not an arbitrary add-zero rule.
Worked example 3 · MATH-5B-C09-L06-Q03
Estimate, then calculate 0.008 ÷ 1000.
Solution: 0.000008
÷ 1000 changes each digit’s unit by 1000. Example 0.008 ÷ 1000 = 0.000008. This is not an arbitrary add-zero rule.
Check understanding
1 · MATH-5B-C09-L06-Q04
Calculate 0.048 ÷ 10; explain the place-value change.
Show worked answer (after attempting)
Answer: 0.0048
÷ 10 changes each digit’s unit by 10. Example 0.048 ÷ 10 = 0.0048. This is not an arbitrary add-zero rule.
2 · MATH-5B-C09-L06-Q05
A measurement is 3.206 kg. What is 3.206 ÷ 100?
Show worked answer (after attempting)
Answer: 0.03206 kg
÷ 100 changes each digit’s unit by 100. Example 3.206 ÷ 100 = 0.03206. This is not an arbitrary add-zero rule.
3 · MATH-5B-C09-L06-Q06
Estimate, then calculate 0.009 ÷ 1000.
Show worked answer (after attempting)
Answer: 0.000009
÷ 1000 changes each digit’s unit by 1000. Example 0.009 ÷ 1000 = 0.000009. This is not an arbitrary add-zero rule.
Guided practice
1 · MATH-5B-C09-L06-Q07
Calculate 0.049 ÷ 10; explain the place-value change.
Show worked answer (after attempting)
Answer: 0.0049
÷ 10 changes each digit’s unit by 10. Example 0.049 ÷ 10 = 0.0049. This is not an arbitrary add-zero rule.
2 · MATH-5B-C09-L06-Q08
A measurement is 3.207 kg. What is 3.207 ÷ 100?
Show worked answer (after attempting)
Answer: 0.03207 kg
÷ 100 changes each digit’s unit by 100. Example 3.207 ÷ 100 = 0.03207. This is not an arbitrary add-zero rule.
3 · MATH-5B-C09-L06-Q09
Estimate, then calculate 0.01 ÷ 1000.
Show worked answer (after attempting)
Answer: 0.00001
÷ 1000 changes each digit’s unit by 1000. Example 0.01 ÷ 1000 = 0.00001. This is not an arbitrary add-zero rule.
4 · MATH-5B-C09-L06-Q10
Calculate 0.05 ÷ 10; explain the place-value change.
Show worked answer (after attempting)
Answer: 0.005
÷ 10 changes each digit’s unit by 10. Example 0.05 ÷ 10 = 0.005. This is not an arbitrary add-zero rule.
Independent practice
1 · MATH-5B-C09-L06-Q11
A measurement is 3.208 kg. What is 3.208 ÷ 100?
Show worked answer (after attempting)
Answer: 0.03208 kg
÷ 100 changes each digit’s unit by 100. Example 3.208 ÷ 100 = 0.03208. This is not an arbitrary add-zero rule.
2 · MATH-5B-C09-L06-Q12
Estimate, then calculate 0.011 ÷ 1000.
Show worked answer (after attempting)
Answer: 0.000011
÷ 1000 changes each digit’s unit by 1000. Example 0.011 ÷ 1000 = 0.000011. This is not an arbitrary add-zero rule.
3 · MATH-5B-C09-L06-Q13
Calculate 0.051 ÷ 10; explain the place-value change.
Show worked answer (after attempting)
Answer: 0.0051
÷ 10 changes each digit’s unit by 10. Example 0.051 ÷ 10 = 0.0051. This is not an arbitrary add-zero rule.
4 · MATH-5B-C09-L06-Q14
A measurement is 3.209 kg. What is 3.209 ÷ 100?
Show worked answer (after attempting)
Answer: 0.03209 kg
÷ 100 changes each digit’s unit by 100. Example 3.209 ÷ 100 = 0.03209. This is not an arbitrary add-zero rule.
5 · MATH-5B-C09-L06-Q15
Estimate, then calculate 0.012 ÷ 1000.
Show worked answer (after attempting)
Answer: 0.000012
÷ 1000 changes each digit’s unit by 1000. Example 0.012 ÷ 1000 = 0.000012. This is not an arbitrary add-zero rule.
6 · MATH-5B-C09-L06-Q16
Calculate 0.052 ÷ 10; explain the place-value change.
Show worked answer (after attempting)
Answer: 0.0052
÷ 10 changes each digit’s unit by 10. Example 0.052 ÷ 10 = 0.0052. This is not an arbitrary add-zero rule.
7 · MATH-5B-C09-L06-Q17
A measurement is 3.21 kg. What is 3.21 ÷ 100?
Show worked answer (after attempting)
Answer: 0.0321 kg
÷ 100 changes each digit’s unit by 100. Example 3.21 ÷ 100 = 0.0321. This is not an arbitrary add-zero rule.
8 · MATH-5B-C09-L06-Q18
Estimate, then calculate 0.013 ÷ 1000.
Show worked answer (after attempting)
Answer: 0.000013
÷ 1000 changes each digit’s unit by 1000. Example 0.013 ÷ 1000 = 0.000013. This is not an arbitrary add-zero rule.
Challenge and error analysis
1 · MATH-5B-C09-L06-ERR1
The assigned question is: “A measurement is 3.213 kg. What is 3.213 ÷ 100?” A learner wrote: “3.213 ÷ 100 = 0.13213. 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: 0.03213 kg
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 0.03213 kg. Recompute from the given data: ÷ 100 changes each digit’s unit by 100. Example 3.213 ÷ 100 = 0.03213. This is not an arbitrary add-zero rule.
2 · MATH-5B-C09-L06-ERR2
The assigned question is: “Estimate, then calculate 0.016 ÷ 1000.” A learner wrote: “0.016 ÷ 1000 = 1.000016. 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: 0.000016
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 0.000016. Recompute from the given data: ÷ 1000 changes each digit’s unit by 1000. Example 0.016 ÷ 1000 = 0.000016. This is not an arbitrary add-zero rule.
Exit check
Exit · MATH-5B-C09-L06-Q19
Calculate 0.053 ÷ 10; explain the place-value change.
Show worked answer (after attempting)
Answer: 0.0053
÷ 10 changes each digit’s unit by 10. Example 0.053 ÷ 10 = 0.0053. This is not an arbitrary add-zero rule.