Form 4 Mathematics Chapter 1

Form 4 Mathematics Chapter 1

2011

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)

(ii)

In a positive number, the non-zero digits are significant figures For example, 13.5 [ 3 significant figures] 2756 [ 4 significant figures] If there are zero in between the non-zero digits, it is considered as significant figures too [ 3 significant figures] For example, 105 200.8 [ 4 significant figures]

(iii) If a zero comes 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. For example, 0.30 [ 2 significant figures]

200.0 [ 4 significant figures] (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! For example, 0.0045 [ 2 significant figures]

0.006005 [ 4 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]

© E-Learning for SPM

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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] nd Tips : 0 is the 2 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] th Tips : Which number if the 4 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 Answer : 20.57 ( correct to 4 significant figures) 5. 0.005613 [2] nd Tips : 6 is the 2 significant figure and the number behind the 6 which is 1 is less than 5. So, dropped the 1 and the 6 remains. Answer : 0.0056 ( correct to 2 significant figures) 6. 1462.02 [3] rd Tips : 6 is the 3 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!


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Performing operations of addition, subtraction , multiplication and division for numbers and state the answer in the given specific significant figures figures Example 1

Solve 56.4 – 56.4 – 6.78 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)


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1.2 Standard Form n

Standard form is used to express a very large or very small numbers in the form of A x 10 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 8 8 that the number is a product of 4.5 with 10 . So the standard form of 450000000 is 4.5 x 10 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. 6 So 2340000 is the multiple of 2.34 x 10

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

6

Answer : 2.34 x 10 (You can check this by typing 2.34 x 10 into your calculator and you will get 2340000 , same as for the question )


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Example 2

Express 0.000035 in standard form. Tips :

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

(which is divided by 10 ),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 -5 to the back, this should be a negative index, which is 10 -5

Answer : 3.5 x 10 ( You can check the answer by typing 0.000035 in your calculator and you -5 will get 3.5 x 10 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! n

How to convert A x 10 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 10

6

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. © E-Learning for SPM

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Answer : 4.37 x 10

6

2011

= =

437000 (You can check this by pressing 4.37 x 10

6

into

your calculator and then press ‘=’ . You will get the answer as 4370000! Example 4 -4

Convert 6.78 x 10 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

= -4

= 0.000678 (you (you can type type 6.78 x 10 into your calculator and press shift  ENG,do this TWICE, you will 0

get 0.000678 x 10 as your answer)


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Example 5 Evaluate the value of 3400 it in standard form.



0.0012 , correct it to 2 significant figures and express

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 6 in subtopic 1.1,you will get the answer as 2800000. 2800000 is a multiple of 10 6 for 2.8 and hence the final answer is 2.8 x 10 ( Well, you can check your answer 6 by calculator again by pressing 2.8 x 10 10 and you will eventually get 2800000 as 6 your answer! That’s easy! But remember to express your final answer as 2.8 x 10 (as required by question) 


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Form 4 Mathematics Chapter 1

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