Challenge Express each answer in scientific notation in the...

Challenge Express each answer in scientific notation in the units indicated. a. $\left(1.26 \times 10^{4} \mathrm{kg}\right)+\left(2.5 \times 10^{6} \mathrm{g}\right)$ in kg b. $(7.06 \mathrm{g})+\left(1.2 \times 10^{-4} \mathrm{kg}\right)$ in $\mathrm{kg}$ c. $\left(4.39 \times 10^{5} \mathrm{kg}\right)-\left(2.8 \times 10^{7} \mathrm{g}\right)$ in $\mathrm{kg}$ d. $\left(5.36 \times 10^{-1} \mathrm{kg}\right)-\left(7.40 \times 10^{-2} \mathrm{kg}\right)$ in $\mathrm{g}$

Challenge Express each answer in scientific notation in the units indicated.
a. $\left(1.26 \times 10^{4} \mathrm{kg}\right)+\left(2.5 \times 10^{6} \mathrm{g}\right)$ in kg
b. $(7.06 \mathrm{g})+\left(1.2 \times 10^{-4} \mathrm{kg}\right)$ in $\mathrm{kg}$
c. $\left(4.39 \times 10^{5} \mathrm{kg}\right)-\left(2.8 \times 10^{7} \mathrm{g}\right)$ in $\mathrm{kg}$
d. $\left(5.36 \times 10^{-1} \mathrm{kg}\right)-\left(7.40 \times 10^{-2} \mathrm{kg}\right)$ in $\mathrm{g}$

Key Concepts

Arithmetic Operations with Numbers in Scientific Notation

Performing arithmetic operations with numbers in scientific notation requires aligning the powers of ten when adding or subtracting. Once the exponents are the same, the coefficients can be combined. The final result is then often re-expressed in normalized scientific notation to maintain clarity and standard form.

Consistency of Units in Calculations

Ensuring consistency of units means converting all quantities to the same unit before performing any arithmetic operations. This is important during addition or subtraction to avoid errors and obtain a result that is meaningful and correctly expressed in the chosen unit.

Unit Conversion

Unit conversion involves converting a measurement from one unit to another using appropriate conversion factors. This is crucial when combining or comparing values expressed in different units, such as converting grams to kilograms or vice versa, to ensure that arithmetic operations are consistent and the results are in the desired unit.

Scientific Notation

Scientific notation is a method of writing very large or very small numbers in the form a × 10^n, where a is a coefficient greater than or equal to 1 but less than 10, and n is an integer. This format provides clarity and simplicity when performing calculations or comparing magnitudes in different orders of magnitude.

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