T1_LO4 · lo-yr9-scientific-notation
Scientific notation writes very large or very small numbers compactly as \(a \times 10^{n
\), where $1 \le a < 10$ and $n$ is an integer.}
Steps — large numbers
Move the decimal point left until only one digit remains before it.
Count how many places you moved — that is the exponent $n$.
Write the result as \(a \times 10^{n
\).}
Steps — small numbers
Move the decimal point right until only one non-zero digit is before it.
Count the places moved — that is $-n$.
Write as \(a \times 10^{-n
\).}
Examples
$2000 = 2 \times 10^{3}$ (move 3 left)
$0.00037 = 3.7 \times 10^{-4}$ (move 4 right)
$5 \times 10^{3} = 5000$ (move 3 right)
$7.5 \times 10^{-2} = 0.075$ (move 2 left)
Writing \(30 \times 10^{2
\) instead of $3 \times 10^{3}$. The coefficient must be between 1 and 10. $30$ is too large. Adjust: $30 \times 10^{2} = 3 \times 10^{3}$.}
Write $2000$ in scientific notation.
Write $0.00037$ in scientific notation.
Express $5 \times 10^{3}$ as an ordinary number.
Example 1: large number
Write $9,500,000$ in scientific notation.$$ 9 500 000 $$Move the decimal point 6 places left: $9.5$. Answer: \(9.5 \times 10^{6
\).}
Example 2: small number
Write $0.00012$ in scientific notation.$$ 0.00012 $$Move the decimal point 4 places right: $1.2$. Answer: \(1.2 \times 10^{-4
\).}
Convert $3.84 \times 10^{5}$ to a normal number.
Write $0.02$ in scientific notation.
Write $7.5 \times 10^{-2}$ as a decimal.
Example 3: multiplying in sci. not.
Calculate \((3 \times 10^{4
) \times (2 \times 10^{3})\).$$ 3 \times 2 = 6 $$$$ 10^{4} \times 10^{3} = 10^{7} $$Answer: $6 \times 10^{7}$.}
Example 4: dividing in sci. not.
Calculate \((6 \times 10^{5
) \div (2 \times 10^{2})\).$$ 6 \div 2 = 3 $$$$ 10^{5} \div 10^{2} = 10^{3} $$Answer: $3 \times 10^{3}$.}
Adding exponents instead of subtracting during division. Remember: divide coefficients, subtract exponents.