Explore · MATH-5B-C10-L03-OPEN
Find one tenth of 7.56 by calculating 7.56 × 0.1.
Great Inheritance Mathematics Term B · Original independent course
Multiplying by 0.1 or 0.01
Watch for: Believing multiplication must make a positive number larger.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C10-L03-PREREQ
What is 1/10 of 20?
Show worked answer (after attempting)
Answer: 2
20 ÷ 10 = 2.
Understand the idea
Interpret multiplication by 0.1 and 0.01 as one-tenth or one-hundredth of a positive number. The essential earlier idea is: 5A fraction multiplication and Chapter 9 decimal equivalence.. The model below will always use the actual quantities from the worked problem. Check believing multiplication must make a positive number larger when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C10-L03-Q01
Find one tenth of 7.46 by calculating 7.46 × 0.1.
Solution: 0.746
0.1 is one tenth. Therefore 7.46 × 0.1 = 0.746, smaller than the starting positive amount.
Worked example 2 · MATH-5B-C10-L03-Q02
A container holds 4.5 L. What is one hundredth of this capacity?
Solution: 0.045 L
0.01 is one hundredth. Therefore 4.5 × 0.01 = 0.045, smaller than the starting positive amount.
Worked example 3 · MATH-5B-C10-L03-Q03
Explain whether 0.83 × 0.1 should be greater or less than 0.83 and calculate.
Solution: 0.083
0.1 is one tenth. Therefore 0.83 × 0.1 = 0.083, smaller than the starting positive amount.
Check understanding
1 · MATH-5B-C10-L03-Q04
Find one tenth of 7.56 by calculating 7.56 × 0.1.
Show worked answer (after attempting)
Answer: 0.756
0.1 is one tenth. Therefore 7.56 × 0.1 = 0.756, smaller than the starting positive amount.
2 · MATH-5B-C10-L03-Q05
A container holds 4.6 L. What is one hundredth of this capacity?
Show worked answer (after attempting)
Answer: 0.046 L
0.01 is one hundredth. Therefore 4.6 × 0.01 = 0.046, smaller than the starting positive amount.
3 · MATH-5B-C10-L03-Q06
Explain whether 0.93 × 0.1 should be greater or less than 0.93 and calculate.
Show worked answer (after attempting)
Answer: 0.093
0.1 is one tenth. Therefore 0.93 × 0.1 = 0.093, smaller than the starting positive amount.
Guided practice
1 · MATH-5B-C10-L03-Q07
Find one tenth of 7.66 by calculating 7.66 × 0.1.
Show worked answer (after attempting)
Answer: 0.766
0.1 is one tenth. Therefore 7.66 × 0.1 = 0.766, smaller than the starting positive amount.
2 · MATH-5B-C10-L03-Q08
A container holds 4.7 L. What is one hundredth of this capacity?
Show worked answer (after attempting)
Answer: 0.047 L
0.01 is one hundredth. Therefore 4.7 × 0.01 = 0.047, smaller than the starting positive amount.
3 · MATH-5B-C10-L03-Q09
Explain whether 1.03 × 0.1 should be greater or less than 1.03 and calculate.
Show worked answer (after attempting)
Answer: 0.103
0.1 is one tenth. Therefore 1.03 × 0.1 = 0.103, smaller than the starting positive amount.
4 · MATH-5B-C10-L03-Q10
Find one tenth of 7.76 by calculating 7.76 × 0.1.
Show worked answer (after attempting)
Answer: 0.776
0.1 is one tenth. Therefore 7.76 × 0.1 = 0.776, smaller than the starting positive amount.
Independent practice
1 · MATH-5B-C10-L03-Q11
A container holds 4.8 L. What is one hundredth of this capacity?
Show worked answer (after attempting)
Answer: 0.048 L
0.01 is one hundredth. Therefore 4.8 × 0.01 = 0.048, smaller than the starting positive amount.
2 · MATH-5B-C10-L03-Q12
Explain whether 1.13 × 0.1 should be greater or less than 1.13 and calculate.
Show worked answer (after attempting)
Answer: 0.113
0.1 is one tenth. Therefore 1.13 × 0.1 = 0.113, smaller than the starting positive amount.
3 · MATH-5B-C10-L03-Q13
Find one tenth of 7.86 by calculating 7.86 × 0.1.
Show worked answer (after attempting)
Answer: 0.786
0.1 is one tenth. Therefore 7.86 × 0.1 = 0.786, smaller than the starting positive amount.
4 · MATH-5B-C10-L03-Q14
A container holds 4.9 L. What is one hundredth of this capacity?
Show worked answer (after attempting)
Answer: 0.049 L
0.01 is one hundredth. Therefore 4.9 × 0.01 = 0.049, smaller than the starting positive amount.
5 · MATH-5B-C10-L03-Q15
Explain whether 1.23 × 0.1 should be greater or less than 1.23 and calculate.
Show worked answer (after attempting)
Answer: 0.123
0.1 is one tenth. Therefore 1.23 × 0.1 = 0.123, smaller than the starting positive amount.
6 · MATH-5B-C10-L03-Q16
Find one tenth of 7.96 by calculating 7.96 × 0.1.
Show worked answer (after attempting)
Answer: 0.796
0.1 is one tenth. Therefore 7.96 × 0.1 = 0.796, smaller than the starting positive amount.
7 · MATH-5B-C10-L03-Q17
A container holds 5 L. What is one hundredth of this capacity?
Show worked answer (after attempting)
Answer: 0.05 L
0.01 is one hundredth. Therefore 5 × 0.01 = 0.05, smaller than the starting positive amount.
8 · MATH-5B-C10-L03-Q18
Explain whether 1.33 × 0.1 should be greater or less than 1.33 and calculate.
Show worked answer (after attempting)
Answer: 0.133
0.1 is one tenth. Therefore 1.33 × 0.1 = 0.133, smaller than the starting positive amount.
Challenge and error analysis
1 · MATH-5B-C10-L03-ERR1
The assigned question is: “A container holds 5.3 L. What is one hundredth of this capacity?” A learner wrote: “5.3 × 0.01 = 0.153. 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: 0.053 L
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 0.053 L. Recompute from the given data: 0.01 is one hundredth. Therefore 5.3 × 0.01 = 0.053, smaller than the starting positive amount.
2 · MATH-5B-C10-L03-ERR2
The assigned question is: “Explain whether 1.63 × 0.1 should be greater or less than 1.63 and calculate.” A learner wrote: “1.63 × 0.1 = 1.163. 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: 0.163
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 0.163. Recompute from the given data: 0.1 is one tenth. Therefore 1.63 × 0.1 = 0.163, smaller than the starting positive amount.
Exit check
Exit · MATH-5B-C10-L03-Q19
Find one tenth of 8.06 by calculating 8.06 × 0.1.
Show worked answer (after attempting)
Answer: 0.806
0.1 is one tenth. Therefore 8.06 × 0.1 = 0.806, smaller than the starting positive amount.