Converting units

This lesson is about changing measurements within a unit family and changing rates built from those units. For time, one hour equals sixty minutes. For length, one kilometre equals one thousand metres, one metre equals one hundred centimetres, and one centimetre equals ten millimetres. These standard multipliers let you move between related units in numerical contexts. Area and volume need more care. Area units use squared scale factors. Since one metre is one hundred centimetres, one square metre is one hundred squared, which is ten thousand square centimetres. Volume units use cubed factors. One cubic metre is one hundred cubed cubic centimetres, which is one million cubic centimetres. Capacity connects too: one litre equals one thousand cubic centimetres. Pause and ask why the factor is squared or cubed. Mass uses one tonne equals one thousand kilograms, and one kilogram equals one thousand grams. For compound units, change the numerator and denominator separately. Write the rate as a fraction, then change the top and bottom in clear steps. For example, ninety kilometres per hour means ninety kilometres divided by one hour. Change kilometres to metres, and hours to seconds, before you divide. Pause and decide what each part becomes. Now work through ninety kilometres per hour. Ninety kilometres is ninety thousand metres. One hour is three thousand six hundred seconds. So the speed is ninety thousand divided by three thousand six hundred, which equals twenty-five metres per second. A speed in metres per second has a smaller numerical value than the same speed in kilometres per hour, so twenty-five is reasonable. Rates of pay change in the same way. Five pounds forty per hour is five hundred and forty pence per hour. Divide by sixty minutes to get pence per minute: five hundred and forty divided by sixty equals nine pence per minute. For prices, compare by changing to a common unit. Pause and check: does your converted rate use the units you intended? Watch for common errors. Do not use a linear scale factor for area: one square metre is ten thousand square centimetres, not one hundred. Do not use a linear factor for volume: one cubic metre is one million cubic centimetres, not one hundred. For compound units, change both parts. When changing from a smaller unit to a larger unit, check whether to divide. Remember these anchors. Standard metric changes cover length, mass and time. Area uses squared scale factors, and volume and capacity use cubed scale factors. Compound units such as speed, prices and rates of pay change by handling the numerator and denominator separately. Always check whether the changed value is reasonable for the units you now have.