Basic Engineering Mathematics, Second Edition (Newnes)
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Each column is added, starting from the right. Thus Take Evaluate The denominator is changed into an integer by multiplying by The numerator is also multiplied by 10 to keep the fraction the same. Convert a 0. When multiplying decimal fractions: i the numbers are multiplied as if they are integers, and ii the position of the decimal point in the answer is such that there are as many digits to the right of it as the sum of the digits to the right of the decimal points of the two numbers being multiplied together.
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Thus i. Division by 16 can. Determine the dimension marked x in the length of shaft shown in Figure 2. The dimensions are in millimetres. A tank contains litres of oil. How many tins containing 0. Percentages are used to give a common standard and are fractions having the number as their denominators. For 25 1 example, 25 per cent means i. A decimal fraction is converted to a percentage by multiplying by Thus, a 1. Convert to mixed numbers: a 1.
It takes 50 minutes to machine a certain part. Calculate the new time taken.
Hence 25 ths of 2 hours. Thus, the masses of the copper, zinc and nickel are 2. Check: 2. Express as percentages, correct to 3 significant figures: 7 19 11 a b c 1 33 24 16 3. When bolts are manufactured, 36 are unsatisfactory. Determine the percentage unsatisfactory. Express: a kg as a percentage of 1 t b 47 s as a percentage of 5 min c If it contains Calculate the percentage overspeed. Determine the masses of the three elements present. Determine the masses of the copper, zinc and nickel in a 3.
A concrete mixture contains seven parts by volume of ballast, four parts by volume of sand and two parts by volume of cement.
How much ore is needed to produce kg of iron? Calculate the possible maximum and minimum length of the screw. The output power of an engine is kW. Assignment 1 This assignment covers the material contained in Chapters 1 and 2. The marks for each question are shown in brackets at the end of each question. Find a the highest common factor, and b the lowest common multiple of the following numbers: A piece of steel, 1. Determine, in centimeters, the lengths of the three pieces. When an index is an integer it is called a power.
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When no index is shown, the power is 1, i. Laws of indices When simplifying calculations involving indices, certain basic rules or laws can be applied, called the laws of indices.
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These are given below. Note that it does not matter whether the 4th root of 16 is found first or whether 16 cubed is found first—the same answer will result. In Problems 1 to 12, simplify the expressions given, expressing the answers in index form and with positive indices: 1. The laws of indices only apply to terms having the same base. To simplify the arithmetic, each term is divided by the HCF of all the terms, i. Dividing each term by the HCF i. Evaluate a b Thus: is written as 5. When a number is written in standard form, the first factor is called the mantissa and the second factor is called the exponent.
Thus the number 5. When the numbers have different exponents, one way of adding or subtracting the numbers is to express one of the numbers in non-standard form, so that both numbers have the same exponent. Thus: 2. Express in standard form, correct to 3 significant figures: a. For example, 2. Express the following numbers, given in standard form, as fractions or mixed numbers: a 2.
Thus: a Numbers having the same exponent can be added or subtracted by adding or subtracting the mantissae and keeping the exponent the same. Thus: 9. For example, 0.
Units used in engineering and science may be made larger or smaller by using prefixes that denote multiplication or division by a particular amount. The eight most common multiples, with. For example, 5 MV. Use a calculator to evaluate the following in engineering notation: 1.
To take account of this an error due to measurement is said to exist. This type of error is known as a blunder.
Answers which do not seem feasible must be checked and the calculation must be repeated as necessary. An engineer will often need to make a quick mental approximation for For example, may be The base b when measured is found to be 3. Determine the area of the triangle. However, it is not usual in a measurement type problem to state the answer to an accuracy greater than 1 significant figure more than the least accurate number in the data: this is 7.
Problem 2. In Problems 1 to 5 state which type of error, or errors, have been made: 1. Hence an order of magnitude error has occurred. Thus a blunder has been made. In Problems 6 to 8, evaluate the expressions approximately, without using a calculator.
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Without using a calculator, determine an approximate value of a. The most modern aid to calculations is the pocket-sized electronic calculator. With one of these, calculations can be quickly and accurately performed, correct to about 9 significant figures. The scientific type of calculator has made the use of tables and logarithms largely redundant. To help you to become competent at using your calculator check that you agree with the answers to the following problems: Problem 4.
Problem 7. Evaluate the following, expressing the answers in standard form, correct to 4 significant figures. In Problems 1 to 3, use a calculator to evaluate the quantities shown correct to 4 significant figures: 1. Evaluate the following, expressing the answers in standard form, correct to 4 decimal places:. Examples include currency exchange rates, imperial to metric unit conversions, train or bus timetables, production schedules and so on.
Currency exchange rates for five countries are shown in Table 4. Some approximate imperial to metric conversions are shown in Table 4.