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Let's solve the three questions:

### a) Write 47,000 in standard form.

To express 47,000 in standard form:
- 47,000 is \( 4.7 \times 10^4 \).
- The decimal point is after the first digit, and we count 4 places after the 4 to reach 47,000.

**Answer: \( 4.7 \times 10^4 \)**.

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### b) Write \( 8.6 \times 10^{-2} \) as an ordinary number.

To convert this to an ordinary number:
- Multiply 8.6 by \( 10^{-2} \) (which means divide by 100).
- \( 8.6 \times 10^{-2} = 0.086 \).

**Answer: 0.086**.

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### c) Work out 51,000 × 3,000 and give your answer in standard form.

First, multiply the numbers:
- \( 51,000 \times 3,000 = 153,000,000 \).

Now convert to standard form:
- \( 153,000,000 = 1.53 \times 10^8 \).

**Answer: \( 1.53 \times 10^8 \)**.

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Would you like more details on any of the steps?

Here are five related questions to explore further:
1. How do you convert large numbers into standard form in general?
2. What are the properties of numbers raised to negative exponents?
3. How would you handle small numbers (e.g., decimals) in standard form?
4. How can you multiply two numbers already in standard form directly?
5. How do exponents affect multiplication and division operations?

**Tip:** When converting to standard form, always ensure that there is exactly one non-zero digit before the decimal point.

a) Write 47000 in standard form. b) Write 8.6 × 10^-2 as an ordinary number. c) Work out 51000 × 3000. Give your answer in standard form.

Solve problems involving standard form and exponents. Learn how to express 47,000 in standard form, convert 8.6 × 10^-2 to an ordinary number, and calculate 51000 × 3000 in standard form. Suitable for Grades 6-8.

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