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LESSON 1 WHOLE NUMBERS AND DECIMALS

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Learning Outcomes By the end of this lesson, you should be able to: ◦ Understand whole numbers. ◦ Round whole numbers. ◦ Add, subtract, multiply and divide whole numbers. ◦ Read and write decimal numbers. ◦ Round decimal numbers. ◦ Add, subtract, multiply, and divide decimal numbers.

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Understand whole numbers The whole numbers are the counting numbers inclusive of 0. For example; 0, 1, 2, 3, 4, 5, 100, 1000 The position of a digit in a number written in standard form determines the actual value the digit represents. The table below shows the place value for various positions.

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continuation Place (underlined)Name of position 1 000Ones (units) 1 000Tens 1 000Hundreds 1 000Thousands 1 000 000Ten thousands 1 000 000Hundred thousands 1 000 000Millions

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Rounding whole numbers. Rule of rounding Identify the position to be rounded. Draw a line under that place. If the digit to the right of the number to be rounded is 5 or more, increase by 1 (round up); if 4 or less, do not change. Change all digits to the right of the number to be rounded to zero

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Activities Round 324 to the nearest hundred. Answer: 300 Round 5, 897 to the nearest thousand. Answer: 6,000 Round 558,024,521 to the nearest ten thousand. Answer: 558, 020,000

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Addition, subtraction, multiplication and division of whole numbers Addition of whole numbers To add whole numbers, each unit should be justified to the right. Example In one week, Maryam earned the following commissions: Monday, RM 124; Tuesday, RM 88; Wednesday, RM 62; Thursday, RM 137; Friday, RM 195. Find her total commissions for the week.

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Contd… Solution: Her total commissions for the week are: RM 124 + RM 88 + RM 62 + RM 137 + RM 195 = RM 606 Subtracting whole numbers To find the difference between two different numbers requires subtracting a number called subtrahend from another number called minuend.

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Contd.. Example In December 2008, the landlord of an apartment received RM 720 from each of eight tenants. After paying RM 2,180 in quit rent, how much money left with landlord? Solution: Total money received by the landlord: RM 720 + RM 720 + RM 720 + RM 720 + RM 720 + RM 720 + RM 720 + RM 720 = RM 5,760

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Contd… Alternatively, RM720 x 8 = RM 5, 760 Total money that the landlord has left is: RM 5,760 – RM 2,180 = RM 3,580 Multiplication of whole numbers Multiplication is considered as a short cut method to add a series of similar values. The output is called product. 3 + 3 + 3 + 3 + 3 = 15 or 3 x 5 = 15

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Example A spa business owner buys three massage beds at RM 1,540 each, five face lifting machine at RM 695 each, and eight magnifying lamps at RM 38 each. Find the total cost of the equipment purchased. Solution: Total cost of the equipment purchased is: (RM 1,540 x 3) + (RM 695 x 5) + (RM 38 x 8) = RM 8,399

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Division of whole numbers Dividing whole numbers will determine how many times one number or a quantity is contained in another. If the divisor does not divide evenly into the dividend, there will be remainder. Example At a recent garage sale, the total sales were RM 584. If the said amount of money is divided equally among four people, Thava, Rosnah, Maria, and Husin, how much each of them received? Solution:

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Decimal Numbers A decimal number is any number written with a decimal point. Decimal points separate the whole units on the left from the decimal units on the right. Whole unit Decimal units 456. 257 Any number written to the right of the decimal point is called a decimal fraction. The place value of the digits to the right of the decimal point is shown below:

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Place (underlined)Name of position. 1Tenths. 01Hundredths. 001Thousandths. 0001Ten thousandths. 00001Hundred thousandths. 000001Millionths. 0000001Ten millionths

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Addition of decimals The decimal system is positional, the value of a digit depends on its position as well as on its numeric value. To add decimal, you must align the decimal points at the same position. Add 9.38, 4.6, 15.927, and 3.087 Solution: 9.38 + 4.6 + 15.927 + 3.087 = 32.994

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Subtraction of decimals Subtraction requires that the decimal points be aligned, similar to addition. Subtract 25.98 from 33.285. Solution: 33.285 - 25.98 = 6.305

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Multiplication of decimals Decimals are multiplied as if they were whole numbers. (It is not necessary to line up the decimal points). Once a multiplied product has been determined, the number of decimal places equals the sum of the decimal places in the factors. Example Multiply 6.34 with 4.62. 6.34 x 4.62 = 29.2908

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Division of decimals When the divisor is a whole number, place the decimal point in the quotient (the answer) directly above the decimal point in the dividend (the number being divided). Then divide as usual. Example 35.52/ 32 = 1. 101 When the divisor contains a decimal fraction, convert the divisor to a whole number.

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