Created By: Mohd Said B Tegoh

Required Basic Mathematical Skills1 700431 000

Rounding off whole numbers to a specified place valueRound off 1 688 to the nearest hundred

Round off 430 618 to the nearest thousand

310060 < 5 00Round off 30 106 correct to thenearest hundred.

Round off 14.78 to the nearest whole number 4.78+115Understand !!!

Required Basic Mathematical Skills1.8520.50

Rounding off whole numbers to a specified number of decimal placesExpress 1.8523 to three decimal places

Express 0.4968 to two decimal places

Round off 5.316 to 1 decimal place5.316

Round off 4.387 to 2 decimal places4.3879+1

Required Basic Mathematical Skills10-210-4

Law of Indices 10m x 10n = 10m + n

10m 10n = 10m - nSimplify the following103 x 10-5

102 106

Very large and very small numbers are conveniently rounded off to a specified number of significant figures The concept of significant figures is another way of stating the accuracy of a measurementSignificant figures refer to the relevant digits in an integer or a decimal number which has been rounded off to a given degree of accuracy

Positive numbers greater than 1 can be rounded off to a given number of significant figures

The rules for determining the number of significant figures in a number are as follows:All non-zero digits are significantfigures2.73 has 3 significant figures1346 has 4 significant figures

The rules for determining the number of significant figures in a number are as follows:All zeros between non-zero aresignificant figures2.03 has 3 significant figures3008 has 4 significant figures

The rules for determining the number of significant figures in a number are as follows:In a decimal, all zeros after any non-zero digit are significant figures 3.60 has 3 significant figures27.00 has 4 significant figures

The rules for determining the number of significant figures in a number are as follows:In a decimal, all zeros before the first non-zero digit arenot significant 0.0032 has 2 significant figures0.0156 has 3 significant figures

The rules for determining the number of significant figures in a number are as follows:All zeros after any non-zero digit in a whole number are not significant unless stated other wise 1999 = 2000 ( one s.f )

The rules for determining the number of significant figures in a number are as follows:All zeros after any non-zero digit in a whole number are not significant unless stated other wise 1999 = 2000 ( two s.f )

The rules for determining the number of significant figures in a number are as follows:All zeros after any non-zero digit in a whole number are not significant unless stated other wise 1999 = 2000 ( three s.f )

State the number of significant figures ineach of the following 4 576

603

25 009

2.10

0.0706

(f) 0.80 435332

Method of rounding off to a specified number of significant figuresIdentify the digit (x) that is to be rounded offIs the digit after x greater than or equal to 5 Add 1 to x x remains unchanged Do the digit after x lie before the decimal point?Replace each digit with zeroDrop the digitsWrite the number according to the specified number of significant figuresYESNOYES (BEFORE)NO (AFTER)

310060 < 5 00Round off 30 106 correct to threesignificant figures.

Round off 0.05098 correct to threesignificant figures.

05.00988 > 5 +105.00981 0

Round off 0.0724789 correct to four significant figures.

07.0247898 > 5 +107.024789

Complete the following table (Round off to) 471004700050 00020 50020 00020 0001 9802 0002 0003.473.5370.170704.004.040.04570.0460.050.06050.0600.060.0007810.000780.0008

Number3 sig. fig.2 sig. fig.1 sig. fig. 47 103 20 464 1 978 3.465 70.067 4.004 0.04567 0.060450.0007805

We usually use standard form for writing very large and very small numbersA standard form is a number that is written as the product of a number A (between 1 and 10) and a power of 10 A x 10n, where 1 A < 10, and n is an integer

Positive numbers greater than or equal to 10 can be written in the standard formA x 10n , where 1 A 10 and n is the positive integer, i.e. n = 1, 2, 3, Example58 000 000 = 5.8 x 107

Positive numbers less than or equal to 1 can be written in the standard formA x 10n , where 1 A 10 and n is the negative integer, i.e. n = ..,-3, -2, -1 Example0.000073 = 7.3 x 10-5

Express 431 000 in standard form

431 000 Express the number as a product ofA (1 A < 10) and a power of 10 =4.31Ax100 000Power of 10=4.31x105431 000 =4 3 1 0 0 0 =4.31x1055 is the number of places, the decimal point is moved to the left

0.000709Express the number as a product ofA (1 A < 10) and a power of 10 =7.09AxPower of 10=7.09x10-4Express 0.000709 in standard form

=7.09x

0.000709=Express 0.000709 in standard form

0 . 0 0 0 7 0 9=7.09x10-4-4 is the number of places, the decimal point is moved to the right

Write the following numbers in standard form8.765 x 1033.2154 x 1046.9 x 1067.321 x 10-14.52 x 10-33.76 x 10-51.83 x 10-8

NUMBERSTANDARD FORM87653215469000000.73210.004520.00003760.0000000183

Number in the standard form, A x 10n , can be converted to single numbers by moving the decimal point A(a) n places to the right if n is positive(b) n places to the left if n is negative

Express 1.205 x 104 as a single number

3.405 x 104=3 . 4 0 5 03 4 0 5 0=Move the decimal point 4 places to the right

Express 7.53x 10-4 as a single number

7.53 x 10-4=7 . 5 3 0000=0.000753 Move the decimal point 4 places to the left

Express the following in single numbers

4.863 x 1037.2051 x 1044.31 x 1065.164 x 10-11.93 x 10-32.04 x 10-59.16 x 10-848637205143100000.51640.001930.00002040.0000000916

STANDARD FORMNUMBER

3.25 X 105 = 3250007.14 X 10-5 = 0.00007144537000 = 4.537 X 1060.0000006398 = 6.398 X 10-7

325 X 105 32.5 X 106 3.25 X 107 0.325 X 108 ===

431 X 10-8 43.1 X 10-7 4.31 X 10-6 0.431 X 10-5 ===

Two numbers in standard form can be added or subtracted if both numbers have the same index

a x 10m + b x 10m =(a + b) x 10m a x 10m - b x 10m =(a - b) x 10m

5.3 x 105 + 3.8 x 105 =(5.3 + 3.8 ) x 105 =9.1 x 105 7.8 x 10-2 - 3.5 x 10-2 =(7.8 - 3.5 ) x 10-2 =4.3 x 10-2

Two numbers in standard form with difference indices can only be added or subtracted if the differing indices are made equal

4.6 x 106 + 5 x 105 ===4.6 x 106 + 0.5 x 106 (4.6 + 0.5 ) x 106 5.1 x 106

6.4 x 10-4 - 8 x 10-5 ===6.4 x 10-4 - 0.8 x 10-4 (6.4 - 0.8) x 10-4 5.6 x 10-4

Calculate 3.2 x 104 6.7 x 103. Stating your answer in standard form.

_

When two numbers in standard form are multiplied or divided, the ordinary numbers are multiplied or divided with each otherWhile their indices are added or subtracted

a x 10m x b x 10n =(a x b) x 10m + n a x 10m b x 10n=(a b) x 10m - n

9.5 x 103 x 2.2 x 102 =(9.5 x 2.2) x (103 x 102)=20.9 x 103+2 =20.9 x 105 =2.09 x 106

Calculate 1.17 x 10-2 . Stating your answer in 3 x 106standard form.

Calculate , expressing the answer

in standard form.

1 km2 = (1000 x 1000) m2

= (103 x 103) m2

= 106 m2

The area of a piece of rectangular land is 6.4 km2. If the width of the land is 1600 m, calculate the length, in m, of the land Length of the land = Area Width

Round off 0.05098 correct to threesignificant figures.

A 0.051B 0.0500C 0.0509D 0.051005.00988 > 5 +105.00981 0

Round off 0.08305 correct to three significant figures.

A0.083B0.084C0.0830D0.083108.03055 = 5 +108.03051

310060 < 5 00Round off 30 106 correct to threesignificant figures.

A 30 000B 30 100C 30 110D 30 200

Express 1.205 x 104 as a single number

A 1 205B 12 050C 1 205 000D 12 050 00010250

Express 4.23 x 10-4 as a single number

A 0. 423B 0. 0423C 0. 00423D 0. 000423

Express 52 700 in standard form.

A 5.27 102 B 5.27 104 C 5.27 102 D 5.27 x 10-4 5.27 x 10457200

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