A positive number in scientific notation is written as a x 10k, where 1 <= a<10 and k in Z. The exponent records the place value; normalise the coefficient after calculating. **Operation** | **Method** | **Example** Multiply | Multiply coefficients; add exponents. | (3 x 105)(4 x 10-2)=1.2 x 104 Divide | Divide coefficients; subtract exponents. | 6 x 10-42 x 103=3 x 10-7 Add or subtract | Express both quantities with the same power of ten. | 4.2 x 106+3 x 105=4.5 x 106 Example 0.000072=7.2 x 10-5. The negative exponent makes the number small; it does not make the number negative. Rewrite a calculator display such as 7.2E−5 as 7.2 x 10-5. Keep full calculator precision during a calculation and round only the final answer as requested.

A positive number in scientific notation is written as \(a\times10^k\), where \(1\le a<10\) and \(k\in\mathbb Z\). The exponent records the place value; normalise the coefficient after calculating.

\((3\times10^5)(4\times10^{-2})=1.2\times10^4\)

\(\dfrac{6\times10^{-4}}{2\times10^3}=3\times10^{-7}\)

Express both quantities with the same power of ten.

\(4.2\times10^6+3\times10^5=4.5\times10^6\)

\(0.000072=7.2\times10^{-5}\). The negative exponent makes the number small; it does not make the number negative.

Rewrite a calculator display such as 7.2E−5 as \(7.2\times10^{-5}\). Keep full calculator precision during a calculation and round only the final answer as requested. Calculator E notation is not acceptable as a final answer.

Standard Form and Compound Interest

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Scientific notation

Scientific notation

Operation	Method	Example
Multiply	Multiply coefficients; add exponents.	\((3\times10^5)(4\times10^{-2})=1.2\times10^4\)
Divide	Divide coefficients; subtract exponents.	\(\dfrac{6\times10^{-4}}{2\times10^3}=3\times10^{-7}\)
Add or subtract	Express both quantities with the same power of ten.	\(4.2\times10^6+3\times10^5=4.5\times10^6\)