Foundation Mathematics Significant Figures and Rounding Module :MA0001NP Foundation Mathematics Lecture Week 2 Significant Figures And Figures

Fractions, Decimals ,Percentage and Ratios Significant Figures and Rounding Fractions, Decimals ,Percentage and Ratios Significant Figures and Rounding Figures

Fractions Any number in the form p/q (q!=0) is called fractions. For example : 2/3,1/4……. Here p is called numerator and q is called denominator. If p is less than q then p/q is called proper fraction . If p is greater than or equal to q then p/q is called improper fraction. 4/22/2017

Fractions… Equivalent fractions: Given a fraction we may be able to express it in a different form . For example: 3/8 and 9/24 are equivalent factors. 3/6 = 18/36 = 27/54 A fraction is in simplest form when there are no factors common to both numerator and denominator . For example: 5/12 4/22/2017

Fractions…. Q1. Express the following factors in simplest form 24/36 , 58/92 , 25/450 , 169/1300 , 24/228 Q2.Express the following fractions to an equivalent fractions having a denominator 30. 3/4 ,7/6 ,24/21, 8/9 , 10/20 4/22/2017

Fractions…. Addition and Subtraction of fractions In order to add or subtract fractions we first rewrite each fraction so that they all have the same denominator called common denominator. For example: 3/5 + 7/2 =3/5*2/2 +7/2*5/5 =6/10 +35/10 =41/10 4/22/2017

Fractions…. Mixed Fraction: The numbers like 3 ¾ is called mixed fraction because it contains a whole number part 3 and a fractional part ¾. Q. Find 1/4 + 2/3 1¾ + 5 ¼ 4½ + 1/3 1/11- 1/2 4/22/2017

Fractions…. Multiplication and Division of Fractions Q. Evaluate each of the followings giving your answer in simplest form 4/9 *3/8 3/4 * 1 ¾ * 3½ 6¼ ÷2½ +5 3¼ ÷1¾ 99/100÷1¼ 4/22/2017

The decimal number system The decimal number system allows us to use the digits 0 to 9 and the place value system to represent numbers of any size. To represent whole numbers we label columns using increasing powers of 10: ×10 ×10 ×10 ×10 Ten thousands Thousands Hundreds Tens Units Explain the place value system for whole numbers. Discuss the example given and ask pupils to tell you the value of each digit in its given position. For example, ask what the 4 is worth. Also stress the importance of the zero place holder. 104 103 102 101 100 For example, 6 4 7 5

The decimal number system To represent fractions of whole numbers in our place value system we extend the column headings in the other direction by dividing by 10. Starting with the tens column we have: ÷10 ÷10 ÷10 ÷10 Hundredths Thousandths Tens Units Tenths Explain the place value system for fractions of whole numbers and ask pupils to explain the function of the decimal point. Make sure that pupils understand that the number shown in the example is read as “forty-eight point naught three five” and not “forty-eight point nought thirty-five”. Again, ask pupils to tell you the value of each digit in its given position. For example, ask what the 3 is worth. Stress the importance of the zero place holder. 101 100 10-1 10-2 10-3 5 3 8 4 For example, The decimal point

The decimal number system Hundreds Hundredths Tens Units Tenths Thousandths 102 101 100 10-1 10-2 10-3 2 4 3 5 7 4 WHOLE NUMBER PART DECIMAL PART The decimal point separates the whole number part from the fractional part. We can think of the number in this example as: 200 + 40 + 3 + 5 10 4 1000 + 7 100 243.574 =

The decimal number system Q1. Express the following Decimal numbers as proper fractions in their simplest form 0.4 , 0.75 , 0.68 , 0.984 , 0.2505 Q2.Express the following as a decimal number 3/10 +7/100 , 8/10 + 3/10000 , 17/1000 + 5/10 4/22/2017

Ratio A ratio compares the sizes of parts or quantities to each other. For example, What is the ratio of red counters to blue counters? red : blue Talk through the points on the slide showing, with reference to the diagram, that the ratio 9 : 3 is equivalent to the ratio 3 : 1. This is the ratio in its simplest form. Compare this to simplifying fractions. Ask pupils what statements they can make about the number of red counters compared with the number of blue counters. For example, ‘the number of blue counters is a third of the number of red counters’ or ‘the number of red counters is three times the number of blue counters’. To distinguish between ratio and proportion you may wish to ask pupils to tell you the proportion of counters that are red (three quarters). Stress that the ratio compares the sizes of parts to each other while proportion compares the sizes of parts to the whole. = 9 : 3 = 3 : 1 For every three red counters there is one blue counter.

Ratio What is the ratio of red counters to yellow counters to blue counters? red : yellow : blue = 12 : 4 : 8 Show that ratios can compare more than two parts or quantities. Explain with reference to the diagram that 12 : 4 : 8 simplifies to 3 : 1 : 2. = 3 : 1 : 2 For every three red counters there is one yellow counter and two blue counters.

Simplifying ratios For example, Ratios can be simplified like fractions by dividing each part by the highest common factor. For example, 21 : 35 ÷ 7 = 3 : 5 For a three-part ratio all three parts must be divided by the same number. For example, Discuss the simplification of ratios. 6 : 12 : 9 ÷ 3 = 2 : 4 : 3

Simplifying ratios with units When a ratio is expressed in different units, we must write the ratio in the same units before simplifying. Simplify the ratio 90p : £3 First, write the ratio using the same units. 90p : 300p When the units are the same we don’t need to write them in the ratio. Stress that ratios should always be expressed using the same units for each part. 90 : 300 ÷ 30 = 3 : 10

Questions Q 1.Simplify the following ratios 60 cm :70 m : 40mm 150 gm : 2kg :300gm 10p :$20 4/22/2017

Questions Q.2 Divide $1250 between A and B in the ratio of 7:3 . Q3. Divide 250 m in the ratio 3:4:2. Q4. Divide the mass of 560 kg in the ratio 3/4 :1/5 Q5.Simplify the ratio 1700m:5100m:17km 4/22/2017

Questions Q6.The ratio of boys to girls in year 10 of a particular school is 6 : 7. If there are 72 boys, how many girls are there? Q7. A citrus twist cocktail contains orange juice, lemon juice and lime juice in the ratio 6 : 3 : 1. How much of each type of juice is contained in 750 ml of the cocktail? 4/22/2017

Percentage A percentage is a fraction whose denominator is 100. For example: 53/100 = 53% The phrase ’ Per cent ’ means out of 100. To convert a fraction to a percentage divide the numerator by the denominator ,multiply by 100 and then label the result as a percentage . For example :5/8 in to percentage = 5/8 * 100 = 62.5% 4/22/2017

Percentage…. To convert a decimal fraction in to a percentage , multiply by 100 and label the result as a percentage. For example: 0.145 to percentage = 0.145 *100=15.5 % To convert a percentage to its equivalent decimal fraction form divide it by 100. For example: 17.5% in to fraction = 17.5/100 = 0.175 4/22/2017

Questions Q1. Calculate 27 % of 120. Q2. A deposit of $1250 increases by 15%. Calculate the resulting deposit. Q3. A bicycle is advertised at $355. The retailer offers 15% festival discount. How much do you pay for the bicycle. 4/22/2017

Questions…. Q4. The price of a Television increases from $ 13000 to $ 17000 .Calculate the percentage increases.(hint: Change percentage=(change/original value) *100 Q5. There are 850 students in a college . Out of them 350 were boys . Calculate the percentage of boys and girls in that college. 4/22/2017

Questions…. Q6. The population of certain town increases from 2 millions to 3 millions during 10 yrs .Calculate the percentage increase in the population of that town during 10 years . Q7. Calculate 29 % of 5800. Q8. A number X is increased by 20 % to form a new number Y. Y is then decreased by 20 % to form a third number Z . Express Z in terms of X. 4/22/2017