**SENTOSAAA**

### Chap 3: Approximation & Estimation - TOPIC (Cheng Shu Yu Mavis)Milo

**Key information in the FACT SHEET**

**Done by : Cheng Shu Yu Mavis S1-01**

**28 Feb 2011**

**11,545**hospital beds and**7,384**doctors for Singapore healthcare system are approximated figures**7 public hospitals**is an exact figure**1,354**dentists in Singapore is an exact figure

*Source***Fotosearch Stock Photography and Stock Footage (2011)Graphic illustration : Hospital bed with small bedside chest of drawers and wqter dripper and it appears as a image file)Stock Illustration-Hospital Bed. Retrieve from**http://www.fotosearch.com/illustration/hospital-bed.html

Monash University (2011)(Graphic Illustration : Drawing of hospital under category : shops and places and it is a clipart)Korean Language Education Clearinghouse Clipart.Retrieved from http://arts.monash.edu.au/korean/klec/clipart/index.php?RollID=clipart001&FrameID=klec2003-c018

So it goes in Shreveport blog( Graphic Illustration : A clipart of a doctor looking at a clipboard)Article about One Doctor's Perspective of ObamaCare by PAT AUSTIN. Retrieved from : http://soitgoesinshreveport.blogspot.com/2009/08/one-doctors-perspective-of-obamacare.html

Acclaim Images( Graphical Illustration : Clipart picture of a doctor's bag and the contents )Royalty Free Clip Art Images. Retrieved from : http://www.clipartguide.com/_pages/0511-0811-1717-0450.html

Acclaim Images ( Graphical Illustration : Clipart of a african american dentist attending to a female patient ) Royalty FreeClip art Images . Retrieved from : http://www.clipartguide.com/_pages/0511-0905-

2017-2755.html

Ministry of Health , Singapore ( 2007) Hospitals HealthCare Services References Retrieved 28 February 2011 , from the Ministry of Health Singapore website : http://www.moh.gov.sg/mohcorp/hcservices.aspx?id=394

Ministry of Health , Singapore ( 2007) Hospital Healthcare Institution Statistics References. Retrieved 28 February 2011 from the Ministry of Health Singapore website : http://www.moh.gov.sg/mohcorp/statistics.aspx?id=242

### Chapter 3: Approximation & Estimation - Youth Olympic Games (by Jonathan)

Facts and figures:

**3,600 (estimate)**young athletes between 14 and 18 years of age

**5,000 (estimate)**young athletes and officials

**204**National Olympic Committees

**1,200 (estimate)**media representatives

**20,000 (estimate)**local and international volunteers

**370,000 (estimate)**spectators

### Chap 3: Approximation & Estimation - Universal Studios Singapore (by Nina Ding)

**Key information in the FACT SHEET**

**5000**people is an approximated figure**13000**is an approximated figure**7**movie-themes is an exact figure**18**rides and shows is an exact figure

### Chapter 3- Approximation and Estimation- YOG Singapore by Wang Yi Chieh

### Chap 3: Approximation & Estimation - Universal Studio, Singapore (Gladys, DOMO)

**Key information in the FACT SHEET**

- More than
**2 million**of visitors are approximated figures **S$6.59 billion**spent to built the destination is an approximated figure**7**different themed is an exact figure**Opens 9**hours is an exact figure

### Approximation and Estimation of Bukit Timah Reserve (By Lam Jiajun)

### Chap 3: Approximation & Estimation - National holidays & festivals (Mark)

- 25th December is an exact number.
- Two is an exact number
- 1 month is an approximate number
- 100 years is an approximate number.

### Chap 3: Approximation & Estimation - Universal Studios Singapore (by Qian Hui)

### Changi Airport(Ng Ying Liang)

### Approximation , Estimation- Changi Airport (Matthew Yap)

**Done by: Matthew Yap**

**Key information for Fact Sheet****24 Hours 7 days is an exact number.**

**4 and 9 are exact numbers.**

**200 is an approximate number.**

**13% is an approximate number.**

*Source:*

*http://www.changiairport.com/home*

*Pictures obtained from:*

*http://www.mynetbizz.com/pages/singapore/singapore-changi-airport-terminal3.cfm*

*http://www.betateck-eg.com/automation_security.htm*

### Chap 3: Approximation & Estimation -The ArtScience Museum (by Liew Wei Siew)

### Chapter 3: Approximation & Estimation (TASK) Knowing Singapore

*You are going to create a 'FACT SHEET' for one of the following:*

- Singapore at a Glance
- Transportation in Singapore
- Education in Singapore
- National Holidays and Festivals
- Singapore Health Care Services: Hospital Care Services
- Public Utilities Board: Water for All
- Event: National Day Parade
- Event: Youth Olympics Game Singapore 2010
- Event: Asian Youth Games Singapore 2009
- Event: F1 Formula Singapore Grand Prix
- Event: Singapore Chingay
- Attraction: The Singapore Flyer
- Attraction: The Singapore Zoo
- Attraction: The Esplanade
- Attraction: Singapore Changi Airport
- Attraction: National Museum of Singapore
- Attraction: Bukit Timah Nature Reserve
- Attraction: Universal Studio, Singapore
- Attraction: The ArtScience Museum
- Attraction: Jurong Bird Park
- Attraction: Marina Bay
- Attraction: Pulau Ubin
- Attraction: Sentosa

- Click at the hyperlink (above) related to the topic that you have been assigned to.
- Identify
**at least 4 pieces of quantitative information**, amongst them**2 must be exact while 2 are estimated figures**. - Organise the information in the keynote slide.
- Include relevant images to bring out the 'flavour' of the topic that you are assigned to.
- Save the slide as an image: FILE > EXPORT > select IMAGES > Next... to save on the desktop.
- Submit your image as a post in the Class Maths Blog (as a co-author)
- Title of the Post:
**Chap 3: Approximation & Estimation - TOPIC (by Your Name)** - Remember to cite the website which you make reference to.
- Add the label "Approximation, Estimation"

**To be submitted in by the end of the day 2359h.**

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

**There is an example:**

**Key information in the FACT SHEET**

**42%**of women and**55%**of men are approximated figures**11 million**is an approximated figure**20**sports & recreation centres is an exact figure**24**swimming complexes is an exact figure

*Source:*

### Chapter 3: Estimation in Real Life

**Example 1**

With reference to the news article:

- Some numbers in this report are exact figures, some are not... any idea which is which?
- Make a guess, how did the authority get the figure "1,053,000 people"?

~~~~~~~~~~~~~~~~~~~~~

**Example 2**

With reference to the news article:

www.channelnewsasia.com

- Why, in the first case, the exact figure was reported while in the 2nd case, only an estimated figure is given?
- What is the VALUE of using exact figure in the first case?

~~~~~~~~~~~~~~~~~~~~~

**Example 3**

With reference to the news article:

www.channelnewsasia.com

The news reported 800,000 went to the event. How did the organiser measure the number of people? Is this an accurate number?

Click at the permlink to read the responses in Facebook.

~~~~~~~~~~~~~~~~~~~~~

**Example 4**

With reference to the news article:

www.channelnewsasia.com

- How does the organiser track the number of visitors?
- Is it important for the organiser to track the number of visitors in this event?
- Is it important for the organiser to report the exact number of visitors to the event?

### Chapter 3: Approximation and Estimation - An Introduction (Preparation)

**Approximation**&

**Estimation**?

On your own, go through the learning activity in the following website

http://www.s-cool.co.uk/gcse/maths/approximations

At the end of the 'visit', you should be able to tell the difference between approximation and estimation, and when each is used in real world...

### HOME PLAY: End-of-Term 1 Week 8

**1. Chapter 2 Assignment 2**

We attempted the following questions during lesson this week:

Tier B: Q9 to Q13

Tier B: Q15

Complete the remaining questions.

Attach the question paper as the cover of the Assignment.

Deadline: 4 March 2011 (Friday)

**2. Diagnostic Activity**

This is administered via the Ace Learning portal and is now available.

Deadline: 26 February 2011, Saturday 2355h

**3. Preparation for Chapter 3**

- Please read Chapter 3 in your textbook.
- Check inbox in Acelearning portal on readings assigned.

**4. Chapter 2 Assignment 1: Tier C - Questions, 11, 12 & 13**

The discussion of the 3 questions would take place in the "Mathematics in Real Life" Page @ Facebook.

You may refer to the "documents" on the right of the page to participate in the discussion of the answers. The final answer would also be highlighted there.

### Chapter 2: What's the question if you know the answer?

City | Mon | Tues | Wed | Thurs | Fri |

Maximum Temperature ( ^{o}C) | - 8 | 0 | 6 | 1 | 10 |

Minimum Temperature ( ^{o}C) | - 14 | - 6 | - 3 | - 1 | 3 |

**1. What's the question if the answer is Monday and Tuesday?**

**2. What's the question if the answer is 0**

^{o}C?**3. What's the question if the answer is Friday?**

**4. What's the question if the answer is -14**

^{o}C### Chapter 1: Factors and Multiples... Assignment 2

**Tier A**

Q1: There are several possible answers (as discussed in class)

Two possible numbers could be 84 and 504

Q2(a)(i) 216000 = 2^6 x 3^3 x 5^3 (ii) 518400 = 2^8 x 3^4 x 5^2

Q2(b)(i) 216000 = 60 x 60 x 60; cube root of 216000 = 60

Q2(b)(ii) 518400 = 720 x 720; square root of 518400 = 720

Q2(b)(iii) HCF = 43200

Q2(b)(iv) LCM of 60 and 720 = 720 (since 720 is also a multiple of 60)

Q3(i) 322

Q3(ii) 978

**Tier B**

4(a) 2^6 x 5^6

4(b) 1000

4(c) 100

Q5(i) 7

Q5(ii) 100

### Chapter 2: Real Numbers... Assignment 1

Q1(ii) - 1/36 or 0.027 (recurring decimal)

Q2: -16

Q3(i) Statement is correct - both LHS and RHS are -3

Q3(ii) Statement is incorrect - 0 divided by -4 is zero

Q3(iii) Statement is incorrect - since LHS is negative while RHS is +ve

Q3(iv) Statement is correct - both LHS and RHS = 25

Q3(v) Statement is correct - both LHS and RHS are -17

Q3(vi) Statement is incorrect - LHS is 2 while RHS = 8, hence LHS < RHS

Note: LHS is left hand side of the equation given, RHS is the RHS of the equation given.

Q4(i) -1 2/5 or -1.25

Q4(ii) -3

Q4(iii) -88

Q5: 50 x 72 + 25 x 60 = 5100 oranges

Q6(i) False

Sqrt(2) is an irrational number. It cannot be expressed as a fraction whereas 1.41421 is finite, and can be expressed as a fraction 141421/100000

Q6(ii) False

Cuberoot(8) is equal to 2, which can be expressed as a fraction, 2/1. It is therefore a rational number.

Q6(iii) False

Pi is an irrational number as it cannot be expressed as a fraction. However, since it is positive, it can be represented on a number line.

Q6(iv) True

Sqrt(3) is an irrational number. It is therefore neither non-terminating nor non-recurring.

Q7(i) -3, -2, -7/4, -5/3, -3/2, -4/3, 0, 1

Q7(ii) pi < 22/7 < sqrt(2) + sqrt(3) < sqrt(10)

Q8(i) (4 x 6 - 3) x 5

Q8(ii) 144 / (24 / 6)

Q9(i) 32

Q9(ii) 158

Q10: 14 days

### Gentle Reminder... when presenting your answers in the test....

Do not write the working continuously.

2. All working must be neatly and clearly written.

No abstract art!

The markers could not read your mind.

3. Complete your answers with the appropriate "units", when applicable.

4. If you need to copy the question, check that you copy correctly.

Do not miss out or change any sign of operation (e.g. instead of +, you copied as -)

5. Label the parts of your answers clearly.

**Remember:**

- Upon receiving your test papers, always 'scan' through the questions and take note of questions that are easy to score.
- Plan your time.

### Answers to 6 AM Quiz (III)

The answers are now available at the end of the post.

Click at the PERMLINK to refer to the answer and explanation.

### Chapter 2: Worksheet 5 - Word Problems (Answers)

This worksheet was given on Tuesday (22 Feb) as homework.

**Complete the worksheet and submit on Thursday (24 Feb).**

You may write your

**answers**

**with complete working**neatly at the back of the worksheet (which is blank) or on a foolcap paper stapled to the question paper.

~~~~~~~~~~~~~~~~~~~~~~~~~~

**Answers for checking...**

1.

**John, Peter, Ken**

- Method - convert all the given 'times' to a common representation (e.g. fractions with the same denominator; fractions) so that you could do a comparison.
- Ascending order means from smallest value to the largest value.
- Show the working.

**19 13/15 litres**or

**19.86 litres**(correct to 2 decimal places)

- Method: Amount of paint needed to paint 1 hall + Amount of paint needed to paint 3 bedrooms
- = 6 2/3 + (3 x 4 2/5)

**1 13/30 h**or

**1 h 26 min**

- Amount of time for basketball = Total amount of time - time for soccer - time for baseball
- = 9 1/2 - 4 2/5 - 3 2/3

**37 1/27 km**or

**37.037 km**(3 decimal places)

- Fraction of distance for walking = 1 - 3/8 - 2/5 (=9/40)
- 9/40 of the distance is equivalent to 8 1/3 km
- 1/40 of the distance would represent 8 1/3 ¸ 9 = 25/26 km
- Therefore the entire distance (covered by train, bus, walking) = 25/26 x 40

### Chapter 1 (Revision): LCM & HCF: Someone asked...

**The HCF and LCM of two numbers are 12 and 5040 respectively. If one of the number is 420, what is the other number?**

If the 2 numbers are A and B, rewriting what we are given:

- HCF of A and B = 12 (which is the same as 2 x 2 x 3)
- LCM of A and B = 5040

In other words, with prime factorisation,

- A =
**2**x**2**x**3**x ? x ? x ... x ? - B =
**2**x**2**x**3**x ? x ? x ... x ? - {where we do not know what are the factors and how many of them at this point}

- 2 )
__A, B__ - 2 )
__A', B'__ - 3 )
__A'', B''__ - ? )
__A''', B''__ __................__

Given that one of the numbers is 420, we would be able to find the factors that this number contributes to the LCM.

- Prime Factorisation of 420 =
**2**x**2**x**3**x 5 x 7 - Now, we know that LCM of A and B, 5040 is equal to
**2**x**2**x**3**x**5**x**7**x ? - The remaining factor: 5040 ÷ (2 x 2 x 3 x 5 x 7) = 12
- Hence the other number is a product of
**2**x**3**x**3**x 12 =**144**

### Maths Level Test: Term 1 Week 8 Thursday (24 February)

### Chapter 2: Diagnostic Activity - Answers

### Chapter 2: Gentle Reminder of Assignment 1

Gentle Reminder: Deadline of this Graded Assignment on this coming Friday (18 Feb 2011) 1230h.

Remember to staple the Question paper on top of the answers written in the foolscap papers.

### Real Numbers - Rational Numbers: Exploring Recurring Decimals

Investigate some other fraction families such as 1/3, 1/7, 1/9, 1/11, 1/13, 1/17, 1/19.

Which category do these number belong to.

Let's use NUMBERS to help us.

Using numbers, express 1/n as decimals (where 0<n<100).

Indicate which of these numbers are Terminating Decimal and which are Recurring Decimals.

**Post the following in your blog (and include the permlink in the comments):**

- Screen capture of the worksheet that shows your answers.
- Name the post:
**Chap 2: Real Numbers - Rational Numbers**

- The following fractions share a common denominator: 1/6, 2/6, 3/6, 4/6, 5/6, 6/6.
- 1/6 is a recurring decimal.
- Janice concluded that all other fractions with denominator are also recurring decimals.
- Do you agree? Explain...

### Numbers Family - Making Connections

• Rational Numbers

• Irrational Numbers

• Integers

• Negative Fractions

• Positive Fractions

• Whole Numbers

• Natural Numbers

• Imaginary Numbers

**(I) Divide and Conquer**

(a) Write down the "definition" of the above "Numbers".

(b) Give examples of each type of numbers.

(c) Submit your findings in Facebook - Class Page.

(d) Include your group name in the posting.

**(II) Putting them together**

(a) Map out the findings in the chart paper to illustrate the relationships of the numbers/ present the information you found.

(b) Put the chart up at the class notice board.

(c) Include your group name on the chart.

Here's an example how to present the map.

### HOME PLAY: End-of-Term 1 Week 6

**1. Real Numbers - Assignment 1**

Date Due: 18 February 2011 (Friday)

Deadline to be followed strictly else there would be penalty to your score.

Tier A & Tier B are compulsory; Make an attempt to do Tier C (which most of you should be capable of).

**2. Online Activities @ Maths Blog**

Activity 1: What does it mean to us?

Activity 2: Groups of which postings are not put up yet (Domo-kun and Mac Spicy)

Activity 3: Let's examine the patterns! (Investigative activity on Multiplication of Integers)

**3. 6 AM Quiz - COMPULSORY**

It will resume on 12 February 6 am.

Answers will be released on 14 February 6 am.

Submissions after the above deadline will not be awarded with points.

All must attempt.

**4. Preparation for Week 7**

We'll be moving into the 4 operations of Integers (Addition, Subtraction, Multiplication and Division, Combined Operations) on Monday. Go through the exercises on your own:

- Textbook: Chapter 2
- Exercise 2.2 (Basic Practice, Further Practice, Maths@Work)
- Exercise 2.3 (Basic Practice, Further Practice, Maths@Work)
- Workbook: Chapter 2
- Basic Practice: No. 1 to No. 10
- Further Practice: No. 11 to 13

If you come across any questions you are not sure how to tackle, send me an email or submit a comment at this post.

### Real Numbers: Activity 1 - What does it mean to us?

*Enter your answers under comment. Label your answers clearly.)*

3. If 20 km denotes a distance of 20 km due east, what denotes a distance of 6 km due west?

4. If 100 represents a gain of $100, what number represents a loss of $150?

5. If we use the integer "5" to represent 5 floors above the ground level, what integer is used to represent 2 floors below the ground level?

~~~~~~~~~~~~~~~~

- 12 km/h means 12 km/h above the speed limit
- 5˚C denotes an increase of 5˚C
- - 6 km
- -$150
- -2

### Real Numbers: Activity 2 - Let's examine the Patterns! ADDITION of Negative Numbers

__Vocabulary List__:

- Numerical Part
- Sign
- Positive
- Negative
- Difference
- Sum
- Same
- Different

### Real Numbers: Activity 3 - Let's examine the Patterns!

2. Using your completed multiplication table, complete the following sentences:

(a) A

**positive**number multiplied by another

**positive**number gives a .......... answer.

(b) A

**negative**number multiplied by another

**negative**number gives a .......... answer.

(c) A

**positive**number multiplied by a

**negative**number gives a .......... answer.

(d) A

**negative**number multiplied by a

**positive**number gives a .......... answer.

3. Complete the following

- (+) x (+) =
- (-) x (-) =
- (+) x (-) =
- (-) x (+) =

- (+) / (+) =
- (-) / (-) =
- (+) / (-) =
- (-) / (+) =

**How to submit your work?**1. Attempt No. 1 using NUMBERS. Post a screen shoot of your work.

2. Answer No. 2 & 3 in the same post.

3. Submit the permlink of your blog post under Comments.

### (20110208) Real Numbers: Activity - Putting them in ORDER

As a group, you shall arrange these numbers in ascending order, using the < or > to help you.

Find the answer together.

Now, divide yourselves into 2 subgroups so that one subgroup will do the VIVA while the other work on the WRITTEN solution.

(A) VIVA

1. You shall describe how you go about finding the solution.

2. Record your solution using PhotoBooth, QuickTime Player or any application. The clip should not be longer than 2 minutes.

3. Post the videoclip into this Maths blog.

(B) WRITTEN Solution

1. Present the solution neatly on a number line on a piece of paper.

2. The numbers should be clearly marked on the number line.

3. Take a picture of answer.

4. Post the photo into this Maths blog (in the same post).

### Real Numbers: Activity - Putting them in ORDER by MILO

### Real Numbers: Activity - Putting them in ORDER by Mac Spicy

Sorry the picture of the number line cannot be posted in the blog.

Explanation:

We first convert all the numbers into decimals and then we order them from the smallest to the largest. Smallest to the left and largest to the right.

### Real Numbers: Activity - Putting them in ORDER by Ze Specs

So an explanation is needed. Hence, here is the explanation.

1) Convert the integers to the same type of number: Fraction, percentage or decimals.

2) In this case, we use decimals. So after converting, we will compare each number and find out the biggest one. In this case, 100% is the largest one.

3) Line up the numbers in ascending order from left to right.

4) So in between the numbers, place the bigger and smaller sign.

**Hard reminder: Do make it represent that the number on the right is larger than the number on the left.

That is the explanation.

thank you.....

Ze Specs

### Chapter 2 (Real Numbers) Integers - Zero Pairs (Basic Concept)

**The sum of an integer and its opposite is ZERO**

**E.g. 1: - 20 + 20 = 0****E.g. 2: 56 + (-56) = 0****E.g. 3: -28 + 28 = 0**

### Chapter 2 (Real Numbers) Integers - Addition of Integers (Basic Concepts)

**Evaluate - 3 + (-2)**

__Rule__:**To add two negative numbers, add their absolute values and take the negative sign for the answer**

**E.g. 1: -25 + (-17) = -42****E.g. 2: -21 + (-21) = -42****E.g. 3: -18 + (-11) = -29**

**~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~**

**Evaluate 3 + (-7)**

__Rule__: To add 2 integers of different signs such that the__negative__integer has a larger absolute value, we find the difference between their absolute value and take the__negative__sign for the answer.**E.g. 1: -17 + 12 = -5****E.g. 2: 52 + (-67) = -15****E.g. 3: -88 + 85 = -3****E.g. 4: 28 + (-82) = -54**

__Rule__: To add 2 integers of different signs such that the__positive__integer has a larger absolute value, we find the difference between their absolute value and take the__positive__sign for the answer.**E.g. 1: -12 + 17 = 5****E.g. 2: -63 + 68 = 5****E.g. 3: 86 + (-53) = 33****E.g. 4: -38 + 83 = 45**

### Chapter 2 (Real Numbers) Integers - Subtraction (Basic Concepts)

**Evaluate - 2 - 6**

*Note: Zero Pairs are introduced.*

**Evaluate - 5 - (-3)**

**Evaluate 5 - (-7)**

*Note: Zero Pairs are introduced.*

### Chapter 2 (Real Numbers) Integers - Multiplication (Basic Concepts)

**2 x 3**(i.e. 2 groups of positive 3)

and

**2 x (-3)**(i.e. 2 groups of negative 3)

**2 x 3 = 6**

**2 x (-3) = -6**

### Chapter 2 (Real Numbers) Integers - Division (Basic Concepts)

**8 ÷ 2**

and

**(-8) ÷ 2**

**8 ÷ 2 = 4**

**(-8) ÷ 2 = -4**

### Re: Homework for 7 Feb 2011

### Maths Assignment 1 (24 Jan - 28 Jan 2011)

Handcopy was given to all on 24 January, while softcopy was available in the GoogleSite (S1-01 page).

This is a graded assignment where marks would be taken into account for the CA (as explained at the end of Term 1 Week 2; also reflected in the curriculum information page i the GoogleSite).

**It is one's responsibility to check for any piece of work to be done (from his/her classmates) even if one is absent from the school.**

**Failure to submit the work on time would result in penalty if scores.**

Up to 2 Feb 2011, work from the following was not received:

**(1) Ishani (2) Shawn Kit (3) Wei Siew (4) Ruoyu**

**Parents would be contacted if work is received from by 7 February 9 am.**

### Square,Cubes and Roots

Solution: 0.0025x 10000 = 25

Prime factors of 25 = 5,5

Square root of 25 = 5

5/10000 = 0.0005

Explanation : We converted the number to whole number so it is easier to use prime factorisation. Then, we find the prime factors of 25 which is 5^2. Next, since we are suppose to find the square root, we grouped it into groups of 2 and the no. is

Question(2): Find the cube root of 0.729.

Solution: 0.729x1000=729

729=3^6

0.729=>0.003^6

Cube root of 0.729 = 0.003^2

= 0.009

Explanation:Since it is harder to use prime factorisation when it is in decimal form, we multiply it by 1000 so it is a whole number.Then, we used the ladder method to find the prime factors of 729 which is 3^6.After that, we converted both numbers to decimals back which is 0.729 and 0.003^6. So, the cube root of 0.729 is 0.003^2 which is 0.009.

Question(3): Find the Cube root of 8/0.125.

Solution: Cube root of 8/0.125 = Cube root of 8 divided by 125/1000

= Cube root of 8 x 1000/125

= Cube root of 8000/125

= Cube root of 64

= 4

Explanation:

Since 8/0.125 is also equal to 8 divided by 125 over 1000, we changed it that form. Then, since 8 divided by 125 over 1000 is also equal to 8 times 1000 over 125 which is 8000 over 125 which is 8000 divided by 125 and the answer is 64. After that, the cube root of 64 is 4 since when we used prime factorisation we will have 2^6. Lastly, we grouped the numbers into groups of 3 and the answer is 4x4x4 which means the cube root of 64 is 4.