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Scientific Notation Operations
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Scientific Notation Operations
Compute each expression. Write answers in scientific notation unless the question asks for an explanation. Show your steps for written-response problems.
Choose the Best Answer
Select one answer for each question.
1.What is (2.6 × 10⁵) + (1.9 × 10⁵)?
- 4.5 × 10⁵
- 4.5 × 10¹⁰
- 4.5 × 10⁴
- 3.5 × 10⁵
2.Find the product (3.0 × 10⁴)(2.5 × 10³).
- 7.5 × 10⁷
- 5.5 × 10⁷
- 7.5 × 10¹²
- 7.5 × 10⁶
3.Evaluate (7.2 × 10⁸) ÷ (2.4 × 10³).
- 3.0 × 10⁵
- 3.0 × 10¹¹
- 4.8 × 10⁵
- 3.0 × 10⁶
4.Which operation(s) require you to rewrite the terms with matching powers of 10 before combining them?
- Addition only
- Subtraction only
- Addition and subtraction
- Multiplication and division
5.Which expression is equal to (4.0 × 10⁻³)(5.0 × 10⁵)?
- 2.0 × 10³
- 2.0 × 10⁻¹⁵
- 9.0 × 10²
- 2.0 × 10⁸
Calculate and Show Your Work
Include enough steps to show how you used the coefficients and powers of 10.
6.Calculate (8.3 × 10⁶) − (2.7 × 10⁶). Give your answer in scientific notation.
7.Multiply (1.5 × 10⁻⁴)(4.0 × 10⁷). Express the result in scientific notation.
8.Divide (8.4 × 10⁻²) by (2.1 × 10⁻⁵). Write the quotient in scientific notation.
9.A science lab records 3.2 × 10⁵ cells in one sample. A second sample has 4 times as many cells. How many cells are in the second sample? Answer in scientific notation.
10.Add (6.4 × 10⁴) and (3.8 × 10³). Give the sum in scientific notation.
Estimate and Explain
Use place value and exponent rules to support your reasoning.
11.Without finding an exact sum, decide whether (4.7 × 10³) + (2.1 × 10²) is closer to 5,000 or 50,000. Explain briefly.
12.Explain why you add exponents when multiplying powers of 10, but first need matching powers of 10 when adding numbers in scientific notation.
13.A student says (5 × 10⁶) ÷ (2 × 10²) equals 2.5 × 10⁸. Identify the error and give the correct quotient.
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