PIETRO, GIORGIO & MAX ROUNDING ESTIMATING, FACTOR TREES & STANDARD FORM

Transcription

1 PIETRO, GIORGIO & MAX ROUNDING ESTIMATING, FACTOR TREES & STANDARD FORM

2 ROUNDING

3 WHY DO WE ROUND? We round numbers so that it is easier for us to work with. We also round so that we don t have to write as much as we would need to.

4 WHY DO WE ROUND? Whichever end of the number line the number you are rounding is closer to, that is your answer. REMEMBER: hallway always round up.

5 NUMBER LINE Lets round 57 to the nearest is in between 50 and 60. It is around here on the number line below. It is closer to 60. Answer:

6 NUMBER LINE Lets round 55 to the nearest is in between 50 and 60. It is around here on the number line below. It s halfway in between 50 and 60, so we round up to 60. Answer:

7 ROUNDING TO THE NEAREST WHOLE NUMBER On the number line put the whole numbers at either end. Eg. Round 7.43 to the nearest whole number. Answer:

8 ESTIMATING

9 WHY DO WE ESTIMATE? It is very common to make a mistake whilst typing the calculations in the calculator. We estimate to make our life easier and to make the answer look mathematically sensible. Also, the answer we get from estimating aren t exact, but very close to actual answer.

10 HOW DO WE ESTIMATE? The calculations must be as simple as possible so that you can do it in your head. Round to an easier number. Use numbers that are sensible and that work nicely.

11 EXAMPLES Example 1 Example 2 Estimate Estimate Round: Round 20 5 Calculate: 800 Calculate: 4 Answer: 800 Answer: 4

12 ESTIMATING DIFFICULT CALCULATIONS

13 BIDMAS!! There may be sometimes in which it will be asked of you to estimate more complex calculations. Remember always the rule of BIDMAS, when you do these.

14 EXAMPLE

15 STANDARD FORM

16 STANDARD FORM Standard form is a way of writing very small and big numbers. Numbers in standard form need always to be written like this: m x 10^n m: is a number n: is the integer between 1 and 10 determined by how far the decimal point has moved

17 WRITING BIG NUMBERS IN STANDARD FORM For example if you have a very big number like You first have to see how many 0 s there are in the number after that you put basically the numbers of the 0 s in the exponent when you write the formula, like this: 9 x 10^7

18 WRITING SMALL NUMBERS IN STANDARD FORM If you want to convert small number in standard form like: 0, You first need to move the number between the decimal places and you also need to make it as close as a whole number your final result should be: 7,8 x 10^-5

19 EXERCISE: Complete in standard form:

20 EXERCISE: Complete in standard form: 1. 0, , , , ,

21 CALCULATION WITH STANDARD FORM In standard form you can also do some calculation some of them are very easy and you can easily do them in your mind but others like for example when the numbers that you need to calculate are different at that point you may need a little it of time or a calculator.

22 CALCULATION IN STANDARD FORM, ADDICTION AND SUBTRACTION: When you have a set of numbers that ask you to be solved by addiction or subtraction you just have to solve them by calculate the result of each set of numbers and then add or subtract them, for example: 1 x 10^1 + 2 x 10^2 = x 10^4-4x 10^3 = 26000

23 CALCULATION IN STANDARD FORM, MULTIPLICATION AND DIVISION With the division and multiplication there are two methods of calculating if the numbers are not the same then you just have to calculate them and then divide or multiply them, but if the numbers are the same then you can apply this formulas. a^m x a^n = a^m + n a^m : a^n = a^m - n

24 EXERCISE: 1. (9,74 x 10^4) + (1,012 x 10^7) 2. (1 x 10^11) - (2,8945 x 10^2) 3. (3,83 x 10^-5) + (4,572 x 10^-6) 4. (8 x 10^-3) - (5,1318 x 10^-4) 5. (5,17018 x 10^-12) + (1, x 10^11)

25 EXERCISE: 1. (1,278 x 10^5) x (2,76 x 10^-7) 2. (6,6 x 10^-30) : (3 x 10^3) 3. (9 x 10^780) x (9 x 10^456) 4. (1,7 x 10^-90) : (1,7 x 10^-60) 5. (4,444 x 10^ ) x (4,444 x 10^-6193)

26 EXERCISE: (2,34 x 10^28) x (2,34 x 10^98) 2,34 x 10^17 (9,99 x 10^798) : (9,99 x 10^98) 9,99 x 10^699

27 FACTOR TREES

28 PRIME NUMBERS A prime number is a number whose only factors are 1 and itself. A factor tree is a tool that breaks down any number ito it s prime number into it s prime factors. A certain number is a prime factorisation is the list of prime numbers or prime factors that you would multiply together to create that certain number.

29 EXAMPLE To factor this out you must find two numbers that multiply together that make 16. There are two numbers that multiply together to make 16. To complete the factor tree you must also find two numbers that multiply together to make four as I have done here.

30 NOW YOU TRY