Subjects algebra

Standard Form Division

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1. **State the problem:** We need to calculate $$\frac{1.2 \times 10^{15}}{3 \times 10^{9}}$$ and express the answer in standard form. 2. **Recall the rule for division of numbers in standard form:** $$\frac{a \times 10^{m}}{b \times 10^{n}} = \frac{a}{b} \times 10^{m-n}$$ 3. **Apply the rule:** $$\frac{1.2 \times 10^{15}}{3 \times 10^{9}} = \frac{1.2}{3} \times 10^{15-9}$$ 4. **Calculate the fraction:** $$\frac{1.2}{3} = 0.4$$ 5. **Calculate the power of ten:** $$10^{15-9} = 10^{6}$$ 6. **Combine the results:** $$0.4 \times 10^{6}$$ 7. **Convert to standard form:** Standard form requires the coefficient to be between 1 and 10, so: $$0.4 \times 10^{6} = 4.0 \times 10^{5}$$ **Final answer:** $$4.0 \times 10^{5}$$