Is 45\times10^{3} in standard form?

No. a=45 is not less than 10. It is 4.5\times10^{4}.

Rule for (a\times10^{m})(b\times10^{n})?

ab\times10^{m+n}, then adjust to standard form.

Rule for \frac{a\times10^{m}}{b\times10^{n}}?

\frac{a}{b}\times10^{m-n}, then adjust to standard form.

How do you add 5\times10^{4} and 3\times10^{3}?

Write with the same power: 5\times10^{4}+0.3\times10^{4}=5.3\times10^{4}.

What does your GDC show for 5.2\times10^{30}, and what must you write?

It shows 5.2E30; write 5.2\times10^{30}.

Going from kg to g, does the exponent go up or down?

Up by 3: grams are smaller, so the number is bigger.

What accuracy is the IB default for answers?

Exact, or 3 significant figures.

1.1 Scientific notationIB Maths: Applications and Interpretation SL: Flashcards

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When is a number in scientific notation?

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When is a number in scientific notation?: When it is $a\times10^{k}$ with $1\le a<10$ and $k$ an integer.
Write $0.000\,072$ in scientific notation.: $7.2\times10^{-5}$
Write $149\,600\,000$ in scientific notation.: $1.496\times10^{8}$
Is $45\times10^{3}$ in standard form?: No. $a=45$ is not less than 10. It is $4.5\times10^{4}$ .
Rule for $(a\times10^{m})(b\times10^{n})$ ?: $ab\times10^{m+n}$ , then adjust to standard form.
Rule for $\frac{a\times10^{m}}{b\times10^{n}}$ ?: $\frac{a}{b}\times10^{m-n}$ , then adjust to standard form.
Write $16\times10^{-3}$ in standard form.: $1.6\times10^{-2}$
How do you add $5\times10^{4}$ and $3\times10^{3}$ ?: Write with the same power: $5\times10^{4}+0.3\times10^{4}=5.3\times10^{4}$ .
What does your GDC show for $5.2\times10^{30}$ , and what must you write?: It shows 5.2E30; write $5.2\times10^{30}$ .
Convert $7.5\times10^{-6}$ m to mm.: $7.5\times10^{-3}$ mm
How many seconds are in one day, in standard form?: $8.64\times10^{4}$ s
Going from kg to g, does the exponent go up or down?: Up by 3: grams are smaller, so the number is bigger.
What accuracy is the IB default for answers?: Exact, or 3 significant figures.

Exam questions on 1.1 Scientific notation

The mass of the Earth is $5.97\times10^{24}$ kg and the mass of the Moon is $7.35\times10^{22}$ kg.
Write down the mass of the Earth in grams, in the form $a\times10^{k}$ where $1\le a<10$ .2 marks
A red blood cell has a diameter of $7.5\times10^{-6}$ m. An adult body contains approximately $2.4\times10^{13}$ red blood cells.
Find the number of red blood cells needed to make a line of length 1 m. Give your answer in the form $a\times10^{k}$ where $1\le a<10$ , correct to 3 significant figures.2 marks
Light travels at $3.00\times10^{8}$ m s $^{-1}$ . The star Proxima Centauri is approximately $4.0\times10^{16}$ m from the Sun.
Find the time, in days, that light takes to travel from Proxima Centauri to the Sun. Give your answer in the form $a\times10^{k}$ , where $1\le a<10$ , correct to 3 significant figures. (There are $8.64\times10^{4}$ seconds in one day.)3 marks

See the full worksheet

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).