Question: a) Write the number 0.000 049 24 in standard form.
b) Write 5.83 \times 10^4 as an ordinary number.
c) Work out \frac{1.8 \times 10^3 \times 5.4 \times 10^4}{4 \times 10^{-5}}
1. **Problem a:** Write the number 0.000 049 24 in standard form.
2. **Step 1:** Identify the decimal number: 0.00004924.
3. **Step 2:** Move the decimal point to the right until only one non-zero digit remains to the left.
4. Moving the decimal point 5 places to the right gives 4.924.
5. **Step 3:** Since we moved the decimal 5 places to the right, the exponent is -5.
6. **Answer a:** $$0.00004924 = 4.924 \times 10^{-5}$$
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7. **Problem b:** Write $$5.83 \times 10^4$$ as an ordinary number.
8. **Step 1:** Multiply 5.83 by $$10^4 = 10000$$.
9. $$5.83 \times 10000 = 58300$$
10. **Answer b:** $$5.83 \times 10^4 = 58300$$
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11. **Problem c:** Work out $$\frac{1.8 \times 10^3 \times 5.4 \times 10^4}{4 \times 10^{-5}}$$.
12. **Step 1:** Multiply the numerators: $$1.8 \times 5.4 = 9.72$$ and $$10^3 \times 10^4 = 10^{3+4} = 10^7$$.
13. So numerator is $$9.72 \times 10^7$$.
14. **Step 2:** Write the denominator: $$4 \times 10^{-5}$$.
15. **Step 3:** Divide the numbers and powers of ten separately:
$$\frac{9.72}{4} = 2.43$$
$$\frac{10^7}{10^{-5}} = 10^{7 - (-5)} = 10^{12}$$
16. **Step 4:** Combine results:
$$2.43 \times 10^{12}$$
17. **Answer c:** $$\frac{1.8 \times 10^3 \times 5.4 \times 10^4}{4 \times 10^{-5}} = 2.43 \times 10^{12}$$