Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**Hannibal lecter****Member**- Registered: 2016-02-11
- Posts: 330

hi,

when we converting

1.034 to percent

it will be in this method :-

34/1000 * 100 = 3.4%

the question is where did we put the integer 1, isn't it will be 1034/1000 as a fraction right??

so the right method should be (1034/1000) * 100 right? why did we only divide 034 over 1000

the full question was her is that because the population grow every year?

it confused me :-

why the example removed the integer 1 ? it sub 1 - 1.034 = 0.34

than it converted 0.34 to >> 3.4%

why this integer removed

*Last edited by Hannibal lecter (2019-09-15 09:50:28)*

Wisdom is a tree which grows in the heart and fruits on the tongue

Offline

**Hannibal lecter****Member**- Registered: 2016-02-11
- Posts: 330

and the question two is very necessary :-

I find in this website a external method not from the book to find the grew rate

https://pages.uoregon.edu/rgp/PPPM613/class8a.htm

when applying this law in my other example in the book

in the year 2009 and 2003

it will be

(15.757-12.853) /12.853 * 100 = 22.5939469385%

and that's true!

but what about the annually grew

what is the number should I divide on this percent to get the annually grew

I mean is it 2009-2003 = 6 ?

should I divide over 6?

because the law say over N years

as we know if I divide the percent result over 6 it will become ( ( 15.757-12.853) /12.853 * 100 ) / 6 = 3.76565782308%

but the annually grew rate is 3.4% not 3.7% as the book mentioned

so what is happen here why I can't apply this law correctly ?

*Last edited by Hannibal lecter (2019-09-15 10:17:36)*

Wisdom is a tree which grows in the heart and fruits on the tongue

Offline

**Hannibal lecter****Member**- Registered: 2016-02-11
- Posts: 330

please admin answer me two question separately because I'm very beginner don't merge the ideas for me it will hard for me to read and unerstand

Wisdom is a tree which grows in the heart and fruits on the tongue

Offline

**Bob****Administrator**- Registered: 2010-06-20
- Posts: 9,358

hi

To work out a percentage increase you have to do this:

[amount of increase] / [original amount] times 100%

eg. The price of something goes up from $20 to $25. What is the percentage increase?

increase = 25 - 20 = 5

% increase = 5/20 x 100 = 25%

In your question the 'old' population is 12.853 M and the 'new' is 13.290 M

So the increase is 13.290 M - 12.853 M = 0.437 M

[note: the 'Millions' = M cancel out here]

% increase = 0.437 / 12.853 x 100 = 3.4%

The question didn't do this calculation; rather

13.290 M / 12.853 M = 1.034

You are wondering how they got the correct percentage from this.

So an easy way to get the % increase from is just to take off the 1 (= 12.853/12.853)

In situations like these taking off the 1 will always work as 1 is the same as 100% which is the original amount before the increase.

The law that you have discovered is the one you should be using … it's the same as the one I used above.

The question calculates the increase for each year compared with the year before.

So every time you should be doing

[old population] / [population one year later] x 100%

The answers I get are

3.399984

3.438676

3.477122

3.486819

3.484818

3.43311

The 'book' has rounded off the answers. They are not exactly the same but near enough to say the growth is a constant percentage.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

Offline

**Hannibal lecter****Member**- Registered: 2016-02-11
- Posts: 330

thanks now everything almost clear thank you very much

you rounded 0.347/12.853 = 0.03399984439 to 0.034

I read the round subject on the site

but I still wonder is that legal to do in every number?

isn't that will make mistakes and arithmetic glitch

I mean when round these numbers ain't they will effect the result and cause a system fail

because this is not accurate, when I would round number and where ? and when and where not?

Wisdom is a tree which grows in the heart and fruits on the tongue

Offline

**Bob****Administrator**- Registered: 2010-06-20
- Posts: 9,358

It depends on the question. Sometimes it is wrong to give too many figures. In the UK GCSE exam, candidates are penalised if they fail to round off sensibly!

In your question population figures are being compared. How accurately could you count a population? The figure could go up or down during the count and the people doing the counting might miss somebody. The question wants to demonstrate that the growth is (approximately) exponential, so two decimal places is quite sufficient to show that.

As a practice, consider how many figures are appropriate in each of these cases:

1. The number of supporters at a football match is counted as 34,567.

2. You want to order some 'ready-mix' concrete to make a good surface to park your car. You calculate the area of the space, multiply by the required depth of concrete and get 12.3678 cubic yards.

3. Do trees for timber grow better if the are closely planted or if they are spread out more? To test this you grow some trees on two plots. For one the trees are planted close together; on the other bigger spaces are left between the trees. Then you measure the height of each tree and the circumference of the trunk. Typical measures are 30.36 feet and 81.5 inches.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

Offline

**Hannibal lecter****Member**- Registered: 2016-02-11
- Posts: 330

be the book said :-

{ show that the population grew by a factor of about 1.034, or 3.4%, every year. Whenever we have a constant growth factor (here 1.034), }

isn't constant growth factor should be only 0.034? without 1

the book saying ( 1.034 or! 3.4% )

isn't he should say ( 0.034 or 3.4%)

and the is the number called exponential factor

so what is the correct to say now pls tell

is the exponential growth say to it ( 0.034 or 3.4% ) or ( 1.034 or 3.4%)

Wisdom is a tree which grows in the heart and fruits on the tongue

Offline

**Bob****Administrator**- Registered: 2010-06-20
- Posts: 9,358

1.034 is a multiplier. New population = old population times the multiplier.

3.4% is the percentage increase. new population = old population + 3.4% of the old population.

So we have two ways of describing the same increase.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

Offline

**Hannibal lecter****Member**- Registered: 2016-02-11
- Posts: 330

Bob wrote:

hi

13.290 M / 12.853 M = 1.034

You are wondering how they got the correct percentage from this.

So an easy way to get the % increase from is just to take off the 1 (= 12.853/12.853)

In situations like these taking off the 1 will always work as 1 is the same as 100% which is the original amount before the increase.

Bob

from this screenshot I'll post in the following please if you may see it I highlighted the value by red color :

so is the number 1 + 0.034 = (1.034) called a growth factor or constant of growth or the exponent? but the exponent is ≈ 2.718?!!?

and why the book used this way? not this regular law the we always use to find percentage increase { [amount of increase] / [original amount] times 100%) }

, to illustrate the meaning of 1.034??

Wisdom is a tree which grows in the heart and fruits on the tongue

Offline

**Bob****Administrator**- Registered: 2010-06-20
- Posts: 9,358

hi,

To work out a new value after a percentage increase you would do this:

old value x percentage = increase

new value = old value plus increase.

So it takes two steps.

example:

Increase $35 by 20%

35 x 20/100 = 7

new value = 35 + 7 = $42

But there is short cut that uses multipliers.

You just add 1 to the percentage which you can probably do 'in your head'.

So the multiplier for a 20% increase is 1 + 20/100 = 1 + 0.2 = 1.2

new value = old value x multiplier = 35 x 1.2 = 42

It's worth using this method, especially if you have a lot of calculation involving the same % increase.

example.

Increase each of these amounts by 15%.

Multiplier = 1.15

Old value = $100 new value = 100 x 1.15 = $115

Old value = $150 new value = 150 x 1.15 = $172.50

Old value = $300 new value = 300 x 1.15 = $345.00

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

Offline

**Hannibal lecter****Member**- Registered: 2016-02-11
- Posts: 330

Bob wrote:

It's worth using this method, especially if you have a lot of calculation involving the same % increase.

Bob

I completely now understand the methods and everything about that multiplier

can you please see this following photo (I highlighted the number in red lines) :-

posted image

the book called this multiplier a growth factor! as you can see,

so is that multiplier the same as exponent? or what is it called

is it right to called it a growth factor

and thanks

*Last edited by Hannibal lecter (2021-12-11 04:20:11)*

Wisdom is a tree which grows in the heart and fruits on the tongue

Offline

**Bob****Administrator**- Registered: 2010-06-20
- Posts: 9,358

Try plotting a graph you = a.b^x for different values of a and b.

You'll find all these have a similar shape.

When the multiplier is x2 the graph is y =a.2^x

So if a = 5 for example, x = 0 gives y = 5

x = 1 y = 10

x = 2 y = 20

x = 3 y = 40

And so on

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

Offline