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5.2 On a typical lightweight bed sheet, there might be about three threads per millimetre, both across and lengthwise. If a sheet for a double bed measured two metres square, that would mean 6,0 × 10 ^{3} threads across plus another 6,0 × 10 ^{3} threads lengthwise. That gives us 1,2 × 10 ^{4} threads, each about two metres long. Calculate how many kilometres of thread it took to make the sheet. Tonight, measure your pillowslip and do the same calculation for it.
5.3 A typical raindrop might contain about 1 × 10 ^{–5} litres of water. In parts of South Africa the annual rainfall is about 1 metre. On one hectare that means about 1 × 10 ^{12} raindrops per year. On a largish city that could mean about 6 × 10 ^{16} raindrops per year, or about 1 × 10 ^{7} drops for every man, woman and child on Earth. How many litres each is that?
5.4 Calculate: (give answers in scientific notation)
5.4.1 $\frac{\mathrm{3,}\text{501}\times {\text{10}}^{-5}}{\mathrm{9,5}\times {\text{10}}^{-8}}+\mathrm{4,3}\times {\text{10}}^{-\text{11}}$
5.4.2 $\frac{\mathrm{3,5}\times {\text{10}}^{6}+\mathrm{1,4}\times {\text{10}}^{-\text{17}}}{\mathrm{3,5}\times {\text{10}}^{6}-\mathrm{1,4}\times {\text{10}}^{-\text{17}}}$
end of CLASS WORK
We use prefixes, mostly from Latin and Greek, to make names for units of measurement. For example, the standard unit of length is the metre . When we want to speak of ten metres, we can say one decametre; one hundred metres is a hectometre and, of course, one thousand metres is a kilometre. One tenth of a metre is a decimetre; one hundredth of a metre is a centimetre and one thousandth is a millimetre. There are other prefixes – see how many you can track down.
Your computer pals will be able to confirm, I hope, that in computers a “kilobyte” is really 1024 “bytes”. Now, why is it 1024 bytes and not 1000 bytes? The answer lies in the fact that computers work in the binary system and not in the decimal system like people. Try to find the answer yourself.
Learning outcomes(LOs) |
LO 1 |
Numbers, Operations and RelationshipsThe learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems. |
Assessment standards(ASs) |
We know this when the learner : |
1.1 describes and illustrates the historical development of number systems in a variety of historical and cultural contexts (including local); |
1.2 recognises, uses and represents rational numbers (including very small numbers written in scientific notation), moving flexibly between equivalent forms in appropriate contexts; |
1.3 solves problems in context including contexts that may be used to build awareness of other learning areas, as well as human rights, social, economic and environmental issues such as: |
1.3.1 financial (including profit and loss, budgets, accounts, loans, simple and compound interest, hire purchase, exchange rates, commission, rentals and banking); |
1.3.2 measurements in Natural Sciences and Technology contexts; |
1.4 solves problems that involve ratio, rate and proportion (direct and indirect); |
1.5 estimates and calculates by selecting and using operations appropriate to solving problems and judging the reasonableness of results (including measurement problems that involve rational approximations of irrational numbers); |
1.6 uses a range of techniques and tools (including technology) to perform calculations efficiently and to the required degree of accuracy, including the following laws and meanings of exponents (the expectation being that learners should be able to use these laws and meanings in calculations only): |
1.6.1 x ^{n} × x ^{m} = x ^{n + m} |
1.6.2 x ^{n} x ^{m} = x ^{n – m} |
1.6.3 x ^{0} = 1 |
1.6.4 x ^{–n} = $\frac{1}{{x}^{n}}$ |
1.7 recognises, describes and uses the properties of rational numbers. |
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