1.1 Scientific notationIB Maths: Analysis and Approaches SL: Flashcards

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What form must a number in scientific notation take?

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What form must a number in scientific notation take?: $a\times10^{k}$ where $1\le a<10$ and $k$ is an integer.
Write $0.000\,72$ in scientific notation.: $7.2\times10^{-4}$
Write $306\,000$ in scientific notation.: $3.06\times10^{5}$
Is $23\times10^{4}$ in scientific notation?: No — $23\ge10$ . It should be $2.3\times10^{5}$ .
Simplify $(3\times10^{4})(4\times10^{-7})$ .: $12\times10^{-3} = 1.2\times10^{-2}$
Simplify $\frac{6\times10^{5}}{1.2\times10^{-2}}$ .: $5\times10^{7}$
What must you do before adding $2.1\times10^{6}$ and $4\times10^{5}$ ?: Write them with the same power of 10: $2.1\times10^{6} + 0.4\times10^{6} = 2.5\times10^{6}$ .
A calculator shows 4.1E-8. How must you write this?: $4.1\times10^{-8}$ — calculator notation is not accepted.
If the front number is multiplied by 10, what happens to the exponent?: It decreases by 1, so the value stays the same.
How many significant figures does $6.02\times10^{23}$ have?: 3 (the digits 6, 0, 2).
Evaluate $10^{-6}\div10^{-9}$ .: $10^{3}$
Why might a calculated number of days be rounded up rather than to the nearest whole number?: Because the event (e.g. storage becoming full) only happens part-way through the next day; rounding must suit the context.