Convert to/from scientific notation, compare, and operate on such numbers.
Free, timed SHSAT practice sets on scientific notation— every question includes a full worked explanation, and there's no account required.
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A number in scientific notation has the form \(a \times 10^{n}\), where \(a\) is at least 1 and less than 10.
To standard form: the exponent tells you how many places to move the decimal point.
To scientific notation: put the point after the first nonzero digit, then count how many places it moved. For 62,000,000 the point moves 7 places left, so it is \(6.2 \times 10^{7}\). For 0.00067 the point moves 4 places right, so it is \(6.7 \times 10^{-4}\).
Common traps:
Move the decimal point 3 places right: \(3.6 \times 10^{3} = 3600\). Moving the decimal point one place too many gives \(36000\). Moving the decimal point one place too few gives \(360\). Moving the decimal point 3 places left instead gives \(0.0036\).
Move the decimal point 4 places left: \(4.3 \times 10^{-4} = 0.00043\). Moving the decimal point one place too many gives \(0.000043\). Moving the decimal point one place too few gives \(0.0043\). Moving the decimal point 4 places right instead gives \(43000\).
Place the decimal point after the first nonzero digit: mantissa 1.1. Count how many places it moved from the end of 110,000 to get the exponent 5: 110,000 = \(1.1 \times 10^{5}\). (Using the number of digits, 6, as the exponent gives \(1.1 \times 10^{6}\). Counting one place too few gives \(1.1 \times 10^{4}\). \(11 \times 10^{4}\) has the same value, but it is not scientific notation because \(11\) is not less than 10.)