Mathematics (Chapter 1- Numbers and Language)
Introduction on numbers
Numbers are arithmetic values represented using symbols.
Types of Numbers
Natural Numbers
Natural numbers include all the whole numbers excluding the number 0.
Whole Numbers
Numbers from 0 to ∞
Integers
All the Negative and Positive Whole Numbers
Rational Numbers
All the numbers that can be terminated and recurring
All numbers which can be written as fractions
Includes Decimals
Irrational Numbers
All the numbers that cannot be terminated and recurring
All numbers which cannot be written as fractions
Real Numbers
Numbers in the Number line
1,2,3,4
0,1,2,3,4
−3,−2,−1,0,1,2,3,
-1/2, 0.333333....
π,2–√,0.121221222...
F=...,π,2,0.121221222...
Prime and Composite 🔢
A prime number is the one which has exactly two factors, which means, it can be divided by only “1” and itself. But “1” is not a prime number.
3 is a prime number because 3 can be divided by only two number’s i.e. 1 and 3 itself
A composite number has more than two factors, which means apart from getting divided by the number 1 and itself, it can also be divided by at least one integer or number.
12 is a composite number because it can be divided by 1, 2, 3, 4, 6 and 12. So, the number ‘12’ has 6 factors.
largest Composite number with most factors
840
No. of factors
32
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
Coprime Numbers
The coprime-numbers or mutually primes or relatively primes are the two numbers which have only one common factor.
The factors of 14 are 1, 2 and 7
The factors of 15 are 1, 3 and 5.
Factors and multiples
Factors are what we can multiply to get the number. Multiples are what we get after multiplying the number by an integer
HCF and LCM
The H.C.F. defines the greatest factor present in between given two or more numbers
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Directed Numbers
Directed Numbers are numbers with both size and direction; one direction is positive, and the other is negative.
Temperature
Bank statements/ money accounts: having money is shown as positive (+) and owing money or overdrafts are shown as negative (-)
Elevations above and below sea level
Floors below the ground floor in a large building are often labeled as -1, -2 etc
Mathematics Chapter 2 (Limit of Accuracy)
Significant Figures
Significant figures are the number of digits in a value, often a measurement, that contributes to the degree of accuracy of the value.
Example
67098
To 1 significant figure
70000
Approximation
Rounding means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use.
Example
73 rounded to the nearest ten is 70, because 73 is closer to 70 than to 80. But 76 goes up to 80.
Upper and lower bounds
Upper and lower bounds are the maximum and minimum values that a number could have been before it was rounded.
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A rectangle has a width of 4.3 cm rounded to 1 decimal place and a length of 6.4 cm rounded to 1 decimal place.
The smallest number that will round up to give 6.4 is 6.35, this is the lower bound.
The largest number that will round down to give 6.4 is 6.44999… so we say that 6.45 is the upper bound.
6.35
≤
<
6.45
x