Form 4 Mathematics Chapter 1

Form 4 Mathematics Chapter 1 2011

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Chapter 1 : Standard Form

1.1 Significant Figure

What are significant figure? Significant figures are used to denote an exact value of numbers to a

certain specific degree of accuracy . For example : 289 = 300 ( correct to 1 significant figure)

Rules in rounding off a positive number to a given number of significant

figures

(i) In a positive number, the non-zero digits are significant figures

For example, 13.5 [ 3 significant figures]

2756 [ 4 significant figures]

(ii) If there are zero in between the non-zero digits, it is considered as significant figures

too

For example, 105 [ 3 significant figures]

200.8 [ 4 significant figures]

(iii) If a zero comes after a non zero digit in a decimal, it is considered as significant figures

also since it indicates the degree of accuracy where the measurement is taken.



(iv) If a zeros are before a non-zero digit in a decimal which is less than 1, it is not

considered as significant figures!



(v) For the final case, if there are zeros after a non-zero digit for a whole number, it may or may

not be significant figures as it depends on the degree of accuracy required

For example, 600 [ 1 significant figure if the degree of accuracy needed is to nearest hundred]

600 [ 2 significant figures if the degree of accuracy needed is to nearest ten ]

600 [ 3 significant figures if the degree of accuracy is to nearest whole number]



Lets see some example questions now!

For each number, round it off to the number of significant figures indicated in bracket.

1. 5675 [1]

Tips : 5 is the first significant figure, so as required, we need to round it off to 1

significant figure.The number ‘ 6’ is larger than 5, so add 1 to the digit 5 and dropped the

digit 6,7,and 5

Answer : 6000 ( correct to one significant figures)

2. 0.5273 [ 3]

Tips : 7 is the 3 significant figure and not 2(rules no.iv). The digit 3 is smaller than 5, so

dropped it

Answer : 0.527 ( correct to 3 significant figures)

3. 303.27 [2]

Tips : 0 is the 2nd

significant figure. Since the number after 0 which is 3( smaller than 5),

we shall dropped it.

Answer : 300(correct to 2 significant figures) [In this case, this number is considered as

having 2 significant figure as required by the question]. How if the question want 1

significant figure? The answer will still the same, 300. ( This is what rules no.vi means).

Get it?

4. 20.568 [4]

Tips : Which number if the 4th

significant figure? It’s 6. And 8 is larger than 5, so add one

to the number in front of it which is 6 +1, then dropped the 8


5. 0.005613 [2]

Tips : 6 is the 2nd

significant figure and the number behind the 6 which is 1 is less than 5.

So, dropped the 1 and the 6 remains.


6. 1462.02 [3]

Tips : 6 is the 3rd

significant figure. 2, which is the number after 6 is less than 5, so

dropped 2 and 6 remained. The number after the decimal point should be dropped too as

it is also counted as significant figures!

Answer : 1460 ( correct to 3 significant figure)

Caution !!! The answer should not be 146! Imagine, in your pocket, you have RM

1140, and when people asked you how much you have in your pocket, you would say

around RM 1000 and NOT around RM100!



Performing operations of addition, subtraction , multiplication and division

for numbers and state the answer in the given specific significant figures

Example 1

Solve 56.4 – 6.78 + 23.45 and correct the answer to 2 significant figures.

Tips : Calculate this by using a calculator and then round off the answer to 2 significant figures

Answer : 73.07 ( from calculator)

= 73 (correct to 2 significant figures)

Example 2

Calculate the value of 34.3 + 6.78 0.024 and give your answer correct to 3 significant figures.

Tips : Remember ! Do for the division part first and then just proceed with the addition part! And

lastly correct the answer to 3 significant figures

Answer : 34.3 + (6.78 0.024)

= 34.3 + 282.5

= 316.8

= 317 ( correct to 3 significant figures)

Example 3

Evaluate the value of 3.08 100 x 4.5. Correct your answer to 2 significant figures

Tips : Evaluate from left to right and then round off the answer to 2 significant figures

Answer : 3.08 100 x 4.5

= 0.0308 x 4.5

= 0.1386 (From calculator)

= 0.14 (correct to 2 significant figures)



1.2 Standard Form

Standard form is used to express a very large or very small numbers in the form of A x 10n where

A is greater of equal to 1 but less than 10. For instance, 1 A < 10 and n is an integer

Lets look at one example.

How can you express 450000000 in standard form? Very easy! Just look at the number. Observe

that the number is a product of 4.5 with 108 . So the standard form of 450000000 is 4.5 x 10

8

Example 1

Express 2340000 in standard form

Tips : How to get to know whether this should be a positive index or a negative index ? Well,

this number is large and is a multiple of a number. So, from here, we know that this is a positive

index of 10. But to the power of what? Just move the decimal behind the 2340000. to front until

it fulfil the condition of 1 A < 10 , which is 2.34(also count how many times you move the

decimal point from back to front to get 2.34) In this case we have move the decimal point 6 times.

So 2340000 is the multiple of 2.34 x 106

From here, you moved 6 places to obtain 2.34. Hence,

Answer : 2.34 x 106 (You can check this by typing 2.34 x 10

6 into your calculator and you will

get 2340000 , same as for the question )



Example 2

Express 0.000035 in standard form.

Tips : For this case, this should have a negative index since the number is very small

(which is divided by 10n),n is a positive integer. Move the decimal point to the back to

get 3.5(count also the number of places you moved the decimal point)

How many places the decimal point moved to the back? Its 5! So, if the decimal point is moved

to the back, this should be a negative index, which is 10-5

Answer : 3.5 x 10-5

( You can check the answer by typing 0.000035 in your calculator and you

will get 3.5 x 10-5

which is the same as your final answer for this question!)

Understand so far by having this two examples? Well, now we are going to convert

numbers in standard form to a single number!

How to convert A x 10n to a single number ?

Follow these two rules !

If the index n of the power 10 is positive, moves the decimal point in A n

places to the right.

If the index n of the power 10 is negative, moves the decimal point in A n

places to the left.

Example 3

Convert 4.37 x 106 to a single number.

Tips : The index n ,which is 6 is a positive number.So, move the decimal point in

4.37 6 places to to the right.



Answer : 4.37 x 106 =

= 437000 (You can check this by pressing 4.37 x 106 into

your calculator and then press ‘=’ . You will get

the answer as 4370000!

Example 4

Convert 6.78 x 10-4

to a single number.

Tips : Since the index n, which is -4, is a negative number, so move the decimal

point in 6.78 4 places to the left.

Answer : 6.78 x 10-4

=

= 0.000678 (you can type 6.78 x 10-4

into your calculator

and press shift ENG,do this TWICE, you will

get 0.000678 x 100 as your answer)



Example 5

Evaluate the value of 3400 0.0012 , correct it to 2 significant figures and express

it in standard form.

Tips : Do it one by one, change the answer according to the significant figures

needed and then express it in standard form.

Answer : By pressing calculator, you will get 3400 0.0012 = 2833333.333. Now,

correct 2833333.333 to 2 significant figures using the knowledge you have learnt

in subtopic 1.1,you will get the answer as 2800000. 2800000 is a multiple of 106

for 2.8 and hence the final answer is 2.8 x 106 ( Well, you can check your answer

by calculator again by pressing 2.8 x 106 and you will eventually get 2800000 as

your answer! That’s easy! But remember to express your final answer as 2.8 x 106

(as required by question)

Form 4 Mathematics Chapter 1

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