3.2 Multiplying and dividing To multiply and divide by 10, 100, 1000, etc., write the digits in their place value columns. To multiply, move the digits to the left (replacing the numbers on the right with zeros) and to divide move them to the right (putting in a decimal point, and any zeros necessary for the place value). Multiplication and division by whole numbers in general can be carried out by combining this technique with a knowledge of the multiplication tables up to 10. Try some yourself Carry out the following calculations, without using a calculator. (a) A million pound lottery prize minus a three hundred pound administrative charge. 2.5 Measuring capacity The basic metric unit for capacity is the litre, usually denoted by the symbol l (though sometimes an uppercase L is used to avoid confusion with the number 1). In the SI system, units such as cubic metres (m3), cubic centimetres (cm3) and cubic millimetres (mm3) are used. These two systems are linked because: 1 ml = 1 cm3 The animation below i 2.3 Measuring mass The basic SI unit for mass is the kilogram, symbol kg The tonne (t) which is equivalent to 1000 kg and is a metric unit is often used alongside the SI units. The animation below illustrates how to convert between the most commonly used units of mass, the metric tonne (t); the kilogram (kg); the gram (g); the milligram (mg) and the microgram (μg). 2.2 Converting units A great advantage of the metric system of units is that conversion between units within the system is particularly easy. For example, ‘£1 is worth 100p’ is converting one pound into pence. To convert pounds to pence, you multiply by 100. So £2 is 200p, and £2.63 is 263p. (Remember that to multiply by 100, you move the digits two places to the left in the place value table.) To convert from pence to pounds, you need to reverse this process, i.e. to divide by 100 (moving the 2.1.2 Try some yourself Suggest appropriate units for each of the following: (a) the age of the kitten when it is weaned; (b) the distance between one train station and the Try some yourself Contour lines on a map show all the points at a given height above sea level. The lines are drawn for each height at 50-metre intervals, and points below sea level are shown by negative heights. The diagra 1.9 Negative numbers Numbers can be positive or negative, i.e. greater than or less than zero. Negative numbers have several uses; for example, to measure temperatures below zero, such as −3°C (‘minus 3 degrees Celsius’). They are also used to represent debts and overdrawn accounts: a bank balance of −£84.33 means ‘overdrawn by £84.33’. Negative numbers are shown on the number line to the left of 0. The animation below shows −8, −7, − 1.7 Fractions A fraction is written as one number over another (such as Try some yourself What is 370.76 grams in kilograms? There are 1000 grams in a kilogram. 370.76 ÷ 1000 = 0.370 76. So 370.76 g = 0.370 1.5.1 Try some yourself When dividing by 1000, move the digits 3 places to the right (past the decimal point). Divide 202.15 by 1000. What is 202.15 metres in kilometres? 1.5 Decimals Quantities can be smaller than one (such as 0.5 kg) or take values between whole numbers (such as a height of 1.65 metres). Numbers smaller than one are expressed as decimals or as fractions. Decimals are often easier to work with (especially when using a calculator). Decimals are explained in this section, and fractions following that (Section 1.7). Decimals can be indicated on the number line in between whole numbers. 0.5 and 1.65 are indicated on the figure below. 1.4 Number lines It is often useful in mathematics to think of numbers stretched out along the imaginary number line. The diagram below shows part of the number line.
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) and means the top number divided by the bottom number. The top number, 3, is called the numerator and the bottom number, 10, is call
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