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NSWMaths Standard 2Quick questions

Year 11: Measurement

Quick questions on Scientific notation and significant figures for HSC Maths Standard 2

6short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is writing a large number in standard form?
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For a number bigger than 1010, put the decimal point after the first non-zero digit and count the places back to where it started (the right-hand end). The Earth-Sun distance is
What is writing a small number in standard form?
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For a number between 00 and 11, the point moves the other way, to the right, until it sits just after the first non-zero digit, and the power is negative. An atom's radius of
What is reading standard form on a calculator?
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A calculator shows standard form to save space. A display like 6.022E23 or 6.022^23 means 6.022×10236.022 \times 10^{23}, not 6.022236.022^{23}. The E (or a small raised number) stands for "times ten to the power". A display of 4.5E-7 means 4.5×1074.5 \times 10^{-7}.
What are significant figures?
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Significant figures are the digits in a number that carry real information about its size and accuracy, as opposed to zeros that are only holding place value. The rules for which digits count are:
What are rounding to a given number of significant figures?
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To round to nn significant figures, keep the first nn significant digits, then look at the next digit: if it is 55 or more, round the last kept digit up; otherwise leave it. The place-holding zeros (or the power of 1010) are then set to keep the number the right size. For example,
What is wrong sign on the power?
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Large numbers take a positive power, numbers below 11 take a negative power. A negative power does not make the number negative; 2.5×10102.5 \times 10^{-10} is a small positive number.

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