Conversion of units

Hi everyone,welcome to Maths PlayGround,
Today I will be talking about conversion of units.Conversion of units means changing units of different measurements.

For example
100cm=1m
10cm=1dm(decimetre)
45cm=0.45m
456g=0.456kg
45ml=0.045L
Take Note:ATTENTION!PLEASE NOTE THAT some people might be careless and convert it to 0.45l which is WRONG.
For a table of conversion of units,you may visit this website:
http://en.wikipedia.org/wiki/Conversion_of_units

After seeing some examples,lets do a short exercise.

Q1 .67ml=?l
Q2.55g=?kg
Its getting more and more difficult......
Q3.35micrometre=?m
Q4.0.61nanograms=?grams
That's all,hope you all can understand:)

Arithmetic games

Yo,time to crack your brains hard and destroy some brain cells,challenge the following questions if you can,HAHA:)
Q1:
There is 3 people named A,B and C.A walks at a rate of 20m/min,B walks at a rate of 22m/min,while C walks at a rate of 25m/min.One day,A and C walked together from Town A to Town B,while C walked from Town A to Town B.Several minutes later,C met B,another 10 minutes later,C met A.What is the distance between Town A and Town B?

Q2:
There is 4 people,named A,B ,C and D(ps for using very lame names).In year 2008,A is 20 year's old,B is 18 year's old,C is 12 year's old and D is 8 year's old .which year will it be when twice of A and B's age is equivalent to thrice of C and D's age?

Answer will be provided later......................................

Introduction to speed

Speed is the rate of motion or simply the rate of a certain distance travelled.
Speed can be calculated by the following formula:


when v=speed(velocity),x=distance travelled and t =time taken.

Uniform Speed:
Very easy,means the speed maintained the same!

Average Speed:
Lets look at an example,

Mr Tan drives from Town A to Town B one day.He travelled at a speed of 100km/h for 2 hrs and reduces his speed to 40km/h for another hr and finally reached Town B.What is his average speed?

Total hours taken:1+2=3(hrs)
Distance travelled :40+100+100=240(km)
Average speed:240/3 = 80(km)

From the following example,we could see that we can get average speed by using the following formula:

Total Distance Travelled
_________________

Total Time Taken

Hope you will understand the concept of speed better now:)

Percentage and its applicatons

A unit that defines the word percent and explains the meaning of the percent symbol, and shows the relation between percentages and their equivalent fractions and decimals, giving a method for converting one form to the others. Four general types of problems are discussed: 1) finding a percent of a given number, 2) finding what percent one number is of another, 3) finding a number when a percent of it is given, 4) finding what percent greater or smaller one number is than another. The unit then applies the skills to consumer-related problems: sales tax and gratuities, discount, commission, simple interest, and compound interest. Sample problems with detailed solutions are illustrated, and problems to be solved by students are included.
E.g 5/10=50%
0.5=50%
20% of $400=$80
200/1000=20%
Decrease 20% of 100=80
A damaged chair that cost $110 was sold at a loss of 10%. =$110 x 1/10 = $11, loss.
=110 -11=99
A TV's actual price is at $1000, during the Great Singapore Sales, it was sold at a discount of 40%, what is the price now? =60/100x1000=600
A was handphone was priced at $100, it is taxed at 7%gst.What is the actual price of the pen?=$93

Is percentage important in our daily life???
Yes it is, obviously! For example, when a person with completely no knowledge of percentage, will surely be tricked by bad people when they say that they will give him a 50% discount, but in actual fact gave him only for example, 10&. The person will surely not know as he doesn't know how to calculate.
Also, when your boss ask you to calculate this month's profit or loss in percentage, you definetely be in a great headache!!!

Direct and inverse Proportion

Direct Proportion:

When a quantity gets larger or smaller, we say that it changes.

Sometimes a change in one quantity causes a change, or is linked to a change, in another quantity. If these changes are related through equal factors, then the quantities are said to be in direct proportion. Or one might say that the two quantities are directly proportional.

Inverse Proportion：

Probably better stated as a reciprocal proportion, the inverse proportions relates two quantities through factors that are multiplicative inverses. That is, through factors that are reciprocals, such as 3 and 1/3.

What is rate?

A rate is a ratio that expresses how long it takes to do something, such as traveling a certain distance. To walk 3 kilometers in one hour is to walk at the rate of 3 km/h. The fraction expressing a rate has units of distance in the numerator and units of time in the denominator.
Problems involving rates typically involve setting two ratios equal to each other and solving for an unknown quantity, that is, solving a proportion.r
Converting rates:

We compare rates just as we compare ratios, by cross multiplying. When comparing rates, always check to see which units of measurement are being used. For instance, 3 kilometers per hour is very different from 3 meters per hour!
3 kilometers/hour = 3 kilometers/hour × 1000 meters/1 kilometer = 3000 meters/hour
because 1 kilometer equals 1000 meters; we "cancel" the kilometers in converting to the units of meters.

Important:

One of the most useful tips in solving any math or science problem is to always write out the units when multiplying, dividing, or converting from one unit to another.

What is ratio?

A ratio is a comparison of two numbers. We generally separate the two numbers in the ratio with a colon (:). Suppose we want to write the ratio of 8 and 12.
We can write this as 8:12 or as a fraction 8/12, and we say the ratio is eight
Comparing ratio:
To compare ratios, write them as fractions. The ratios are equal if they are equal when written as fractions.
Proportion:
A proportion is an equation with a ratio on each side. It is a statement that two ratios are equal.
3/4 = 6/8 is an example of a proportion.