Number.notebook. January 20, Add ins

Size: px

Start display at page:

Download "Number.notebook. January 20, Add ins"

Evangeline Simon
5 years ago
Views:

Add ins We have LOADS of things we need to know for the IGCSE that you haven't learnt as part of the Bavarian Curriculum. We are now going to shoehorn in some of those topics and ideas.

1 Add ins We have LOADS of things we need to know for the IGCSE that you haven't learnt as part of the Bavarian Curriculum. We are now going to shoehorn in some of those topics and ideas. Number Add ins L.O. scientific notation estimating and rounding (d.p. and s.f.) percentages (including profit and percentiles) Nov 12 11:50 Do you know this number, 300,000,000 m/sec? It's the Speed of light! Do you recognize this number, kg? Scientists have developed a shorter method to express very large numbers. This method is called scientific notation. This is the mass of a dust particle! 1

2 Scientific Notation is based on powers of the base number 10. The number 123,000,000,000 in scientific notation is written as : The first number 1.23 is called the coefficient. It must be greater than or equal to 1 and less than 10. The second number is called the base. It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.23 x the number 11 is referred to as the exponent or power of ten. To write a number in scientific notation: To write a number in scientific notation: Put the decimal after the first digit and drop the zeroes. In the number 123,000,000,000 The coefficient will be 1.23 To find the exponent count the number of places from the decimal to the end of the number. In 123,000,000,000 there are 11 places. Therefore we write 123,000,000,000 as: To write a number in scientific notation: For small numbers we use a similar approach. Numbers less smaller than 1 will have a negative exponent. A millionth of a second is: Rules for Multiplication in Scientific Notation: 1) Multiply the coefficients 2) Add the exponents (base 10 remains) Example: (3 x 10 4 )(2x 10 5 ) = 6 x 10 9 Example: (5 x 10 3 ) (6x 10 3 ) = 30. x x10 6 = 3.0 x 10 7 in scientific notation. Example: (2.2 x 10 4 )(7.1x 10 5 ) = x 10 9 = x

Rules for Division in Scientific Notation: 1) Divide the coefficients 2) Subtract the

) percentages (including profit and percentiles) Example: (6 x 10 6 ) / (2 x 10 3 ) =

5 x 10 3 Main 2: estimating and rounding Main 2: estimating and rounding Decimal

3 Rules for Division in Scientific Notation: 1) Divide the coefficients 2) Subtract the exponents (base 10 remains) Number Add ins L.O. scientific notation estimating and rounding (d.p. and s.f.) percentages (including profit and percentiles) Example: (6 x 10 6 ) / (2 x 10 3 ) = 3 x 10 3 Example: (2 x 10 7 ) / (8 x 10 3 ) = x x10 4 = 2.5 x 10 3 Main 2: estimating and rounding Main 2: estimating and rounding Decimal Places Significant Figures dp sf sf sf Number Add ins L.O. scientific notation estimating and rounding (d.p. and s.f.) percentages (including profit and percentiles) Write these amounts as fractions, decimals a nd percentages: 3

4 A number as a percentage of another number Write these numbers as a percentage of 225: 50 is...% of 200 Finding percentages of numbers What is 45% of 512? A fast food restaurant decided to decrease by 18% the weight of packaging for their regular meals, which weighed 40 grams. Calculate the weight of the new packaging. Compound Interest If I invested 1000 into an account that gives 4% interest on savings A manufacturer buys a machine for The m achine is expected to depreciate by 12% in the first year and by 8.5% each future year. a) how much would be in my account after 1 year? What will be the e xpected value of the machine after 5 years to the nearest 1? b) how much would be in my account after 5 years? 4

5 If I invested 1000 into an account that gives 4% interest on savings, how much money would I have at the end of the year? A shop is having a sale. Each day, prices are reduced by 20% of the price on the previous day. Before the start of the sale, the price of a television is 450. On the first day of the sale, the price is reduced by 20%. Work out the price of the television on a) the first day of the sale b) the third day of the sale. Main 3 : percentages (including profit and percentiles) Main 3 : percentages (including profit and percentiles) Compound Interest Formula What if we took out a loan for 15 Years at a rate of 10%?... and what if the loan was for 5 years, but the interest rate was only 6%? Let's say your goal is to have $2,000 in 5 Years. You can get 10%, so how much should you start with? In other words, you know a Future Value, and want to know a Present Value. So the Formula is: PV = FV / (1+r) n 5

6 Let's say your goal is to have $2,000 in 5 Years. You can get 10%, so how much should you start with? PV = $2,000 / (1+0.10) 5 = $2,000 / = $1, In other words, $1, will grow to $2,000 if you invest it at 10% for 5 years. 6

Learning Plan 3 Chapter 3

Learning Plan 3 Chapter 3 Questions 1 and 2 (page 82) To convert a decimal into a percent, you must move the decimal point two places to the right. 0.72 = 72% 5.46 = 546% 3.0842 = 308.42% Question 3 Write