Chapter 1- Standard Form

Form 4 Mathematics Chapter 1

Chapter 1 : Standard Form1.1

 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.

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]

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)

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 10^8. So the standard form of 450000000 is 4.5 x 10^8

How to convert A x 10

n

to a single number ?Follow these two rules !

Ø If the index n of the power 10 is positive, moves the decimal point in A n places to the right

Ø If the index n of the power 10 is negative, moves the decimal point in A n places to the left