Explore · MATH-5B-C09-L01-OPEN
What fraction and decimal describe 4 thousandth-sized parts of one whole?
Great Inheritance Mathematics Term B · Original independent course
Thousandths
Watch for: Confusing one-thousandth with one-hundredth.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C09-L01-PREREQ
A whole is split into four equal parts. Three are shaded. What fraction is shaded?
Show worked answer (after attempting)
Answer: 3/4
Three of four equal parts = 3/4 of the whole.
Understand the idea
Explain thousandths as one of 1,000 equal parts of a whole and relate tenths, hundredths and thousandths. The essential earlier idea is: 5A fraction unit wholes and equivalent fractions.. The model below will always use the actual quantities from the worked problem. Check confusing one-thousandth with one-hundredth when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C09-L01-Q01
What fraction and decimal describe 1 thousandth-sized parts of one whole?
Solution: 0.001 = 1/1000
Use one fixed whole made of 1,000 equal parts. 1 parts means 1/1000, equal to 0.001.
Worked example 2 · MATH-5B-C09-L01-Q02
A water sample fills 125 of 1,000 equal measuring units. Express the share as a decimal and fraction.
Solution: 0.125 = 1/8
Use one fixed whole made of 1,000 equal parts. 125 parts means 125/1000, equal to 0.125.
Worked example 3 · MATH-5B-C09-L01-Q03
How many thousandths make 0.37 of a whole?
Solution: 0.37 = 37/100
Use one fixed whole made of 1,000 equal parts. 370 parts means 370/1000, equal to 0.37.
Check understanding
1 · MATH-5B-C09-L01-Q04
What fraction and decimal describe 4 thousandth-sized parts of one whole?
Show worked answer (after attempting)
Answer: 0.004 = 1/250
Use one fixed whole made of 1,000 equal parts. 4 parts means 4/1000, equal to 0.004.
2 · MATH-5B-C09-L01-Q05
A water sample fills 128 of 1,000 equal measuring units. Express the share as a decimal and fraction.
Show worked answer (after attempting)
Answer: 0.128 = 16/125
Use one fixed whole made of 1,000 equal parts. 128 parts means 128/1000, equal to 0.128.
3 · MATH-5B-C09-L01-Q06
How many thousandths make 0.373 of a whole?
Show worked answer (after attempting)
Answer: 0.373 = 373/1000
Use one fixed whole made of 1,000 equal parts. 373 parts means 373/1000, equal to 0.373.
Guided practice
1 · MATH-5B-C09-L01-Q07
What fraction and decimal describe 7 thousandth-sized parts of one whole?
Show worked answer (after attempting)
Answer: 0.007 = 7/1000
Use one fixed whole made of 1,000 equal parts. 7 parts means 7/1000, equal to 0.007.
2 · MATH-5B-C09-L01-Q08
A water sample fills 131 of 1,000 equal measuring units. Express the share as a decimal and fraction.
Show worked answer (after attempting)
Answer: 0.131 = 131/1000
Use one fixed whole made of 1,000 equal parts. 131 parts means 131/1000, equal to 0.131.
3 · MATH-5B-C09-L01-Q09
How many thousandths make 0.376 of a whole?
Show worked answer (after attempting)
Answer: 0.376 = 47/125
Use one fixed whole made of 1,000 equal parts. 376 parts means 376/1000, equal to 0.376.
4 · MATH-5B-C09-L01-Q10
What fraction and decimal describe 10 thousandth-sized parts of one whole?
Show worked answer (after attempting)
Answer: 0.01 = 1/100
Use one fixed whole made of 1,000 equal parts. 10 parts means 10/1000, equal to 0.01.
Independent practice
1 · MATH-5B-C09-L01-Q11
A water sample fills 134 of 1,000 equal measuring units. Express the share as a decimal and fraction.
Show worked answer (after attempting)
Answer: 0.134 = 67/500
Use one fixed whole made of 1,000 equal parts. 134 parts means 134/1000, equal to 0.134.
2 · MATH-5B-C09-L01-Q12
How many thousandths make 0.379 of a whole?
Show worked answer (after attempting)
Answer: 0.379 = 379/1000
Use one fixed whole made of 1,000 equal parts. 379 parts means 379/1000, equal to 0.379.
3 · MATH-5B-C09-L01-Q13
What fraction and decimal describe 13 thousandth-sized parts of one whole?
Show worked answer (after attempting)
Answer: 0.013 = 13/1000
Use one fixed whole made of 1,000 equal parts. 13 parts means 13/1000, equal to 0.013.
4 · MATH-5B-C09-L01-Q14
A water sample fills 137 of 1,000 equal measuring units. Express the share as a decimal and fraction.
Show worked answer (after attempting)
Answer: 0.137 = 137/1000
Use one fixed whole made of 1,000 equal parts. 137 parts means 137/1000, equal to 0.137.
5 · MATH-5B-C09-L01-Q15
How many thousandths make 0.382 of a whole?
Show worked answer (after attempting)
Answer: 0.382 = 191/500
Use one fixed whole made of 1,000 equal parts. 382 parts means 382/1000, equal to 0.382.
6 · MATH-5B-C09-L01-Q16
What fraction and decimal describe 16 thousandth-sized parts of one whole?
Show worked answer (after attempting)
Answer: 0.016 = 2/125
Use one fixed whole made of 1,000 equal parts. 16 parts means 16/1000, equal to 0.016.
7 · MATH-5B-C09-L01-Q17
A water sample fills 140 of 1,000 equal measuring units. Express the share as a decimal and fraction.
Show worked answer (after attempting)
Answer: 0.14 = 7/50
Use one fixed whole made of 1,000 equal parts. 140 parts means 140/1000, equal to 0.14.
8 · MATH-5B-C09-L01-Q18
How many thousandths make 0.385 of a whole?
Show worked answer (after attempting)
Answer: 0.385 = 77/200
Use one fixed whole made of 1,000 equal parts. 385 parts means 385/1000, equal to 0.385.
Challenge and error analysis
1 · MATH-5B-C09-L01-ERR1
The assigned question is: “A water sample fills 149 of 1,000 equal measuring units. Express the share as a decimal and fraction.” A learner wrote: “149 parts of the stated whole give a fraction with denominator 100, so my result is 0.249 = 149/1000.” 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: 0.149 = 149/1000
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 0.149 = 149/1000. Recompute from the given data: Use one fixed whole made of 1,000 equal parts. 149 parts means 149/1000, equal to 0.149.
2 · MATH-5B-C09-L01-ERR2
The assigned question is: “How many thousandths make 0.394 of a whole?” A learner wrote: “0.394 parts of the stated whole give a fraction with denominator 100, so my result is 1.394 = 197/500.” 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: 0.394 = 197/500
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 0.394 = 197/500. Recompute from the given data: Use one fixed whole made of 1,000 equal parts. 394 parts means 394/1000, equal to 0.394.
Exit check
Exit · MATH-5B-C09-L01-Q19
What fraction and decimal describe 19 thousandth-sized parts of one whole?
Show worked answer (after attempting)
Answer: 0.019 = 19/1000
Use one fixed whole made of 1,000 equal parts. 19 parts means 19/1000, equal to 0.019.