Indices & Standard Form — Year 9 Practice Questions
Work through these Year 9 practice questions on indices and standard form. Try each one before revealing the worked solution.
Questions
Work out 4⁰.
Write 2⁻³ as a fraction.
Simplify 3⁵ × 3⁻². Leave your answer as a whole number.
Write 0.0005 in standard form.
Write 6 × 10⁻³ as an ordinary number.
Write 8 200 000 in standard form.
Which is smaller: 3 × 10⁻² or 3 × 10⁻⁴?
Light travels about 9.5 × 10¹² km in a year. Write this as an ordinary number.
Answers & Worked Solutions
Question 1 Solution
Step 1: Any non-zero number to the power 0 is 1.
Step 2: So 4⁰ = 1.
Answer: 1
Question 2 Solution
Step 1: A negative index means a reciprocal: 2⁻³ = 1/2³.
Step 2: 2³ = 8, so 2⁻³ = 1/8.
Answer: 1/8
Question 3 Solution
Step 1: Add the indices: 5 + (−2) = 3.
Step 2: 3³ = 27.
Answer: 27
Question 4 Solution
Step 1: Move the point 4 places to make 5.
Step 2: Moving right means a negative power: 5 × 10⁻⁴.
Answer: 5 × 10⁻⁴
Question 5 Solution
Step 1: A power of −3 means move the point 3 places left.
Step 2: 6 becomes 0.006.
Answer: 0.006
Question 6 Solution
Step 1: A = 8.2.
Step 2: The point moves 6 places: 8.2 × 10⁶.
Answer: 8.2 × 10⁶
Question 7 Solution
Step 1: The more negative power is the smaller number.
Step 2: 3 × 10⁻⁴ = 0.0003 is smaller than 3 × 10⁻² = 0.03.
Answer: 3 × 10⁻⁴
Question 8 Solution
Step 1: Move the point 12 places to the right.
Step 2: 9.5 × 10¹² = 9 500 000 000 000 km.
Answer: 9 500 000 000 000 km
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