How to Solve Scientific Notation? (+FREE Worksheet!)

Algebra 1

Scientific Notation

Scientific notation writes very big and very small numbers compactly as a number between 1 and 10 times a power of ten — like \(9.2\times10^7\). Move the decimal, count the places, and you’re done. We’ll convert both directions, with a practice tool and a worksheet maker a tap away.

Tutor-style math help

Introduction to Scientific Notation: what to notice and how to work it

Exponents skill

Exponent rules are shortcuts for repeated multiplication. They work only when the bases and operations match the rule.

What to notice first

Identify the base before touching the exponent. Parentheses can change the base, especially with negative numbers and fractions.

Common student mistake

Do not add exponents unless you are multiplying powers with the same base. For \((x^3)^4\), multiply exponents instead.

Key formulas and cues

\(a^m\cdot a^n=a^{m+n}\)

\(\frac{a^m}{a^n}=a^{m-n}\)

\((a^m)^n=a^{mn}\)

\(a^0=1\text{ for }a\ne0\)

A reliable path

1. Check the baseMake sure the repeated factor is the same.
2. Match the operationMultiplication, division, and powers of powers use different exponent moves.
3. Clean negativesMove negative exponents across the fraction bar and make them positive.

Worked examples

Multiply same bases

Example: \(x^3\cdot x^4\)

1. The base is x in both powers.
2. Multiplication means add exponents.
3. 3 + 4 = 7.

Answer: \(x^7\)

Power of a power

Example: \((y^2)^5\)

1. The whole power is raised to another power.
2. Multiply the exponents.
3. 2 times 5 is 10.

Answer: \(y^{10}\)

Open pop-up practice

Try one before moving on

Try: Simplify \(\frac{x^7}{x^3}\).

Answer: \(x^4\), assuming \(x\ne0\).

Next step: do the matching worksheet or quiz while the method is still fresh, then come back and explain the first step in your own words.

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Introduction to Scientific Notation: pop-up practice

Answer these quick questions, then use the feedback to decide which part of the lesson to review.

Choose an answer to begin.

1. \(a^4\cdot a^2=\)

A\(a^6\)B\(a^8\)C\(2a^6\)

2. \((x^3)^2=\)

A\(x^6\)B\(x^5\)C\(x^9\)

3. \(b^0=\)

A\(1\)B\(0\)C\(b\)

📄 Worksheet Maker✏️ Practice Drills📇 Flashcards

Scientific notation is a compact way to write numbers that are very large or very small, so you don’t have to count long strings of zeros. The distance to the sun and the size of an atom both become short, tidy expressions. It’s built on powers of ten, and once you can slide the decimal point and count places, converting either direction is quick.

In short: a number in scientific notation is written as a coefficient between 1 and 10, times a power of ten — like \(9.2 \times 10^7\). The exponent tells you how many places the decimal moved.

Both Directions

Worked Examples

Slide the decimal, count the places, read off the exponent — traced on each card.

Scientific Notation in the Wild

Scientists live in this notation. The speed of light is about \(3 \times 10^8\) meters per second; a hydrogen atom is roughly \(1 \times 10^{-10}\) meters wide; the U.S. national debt and a cell’s mass are both far easier to write — and compare — as powers of ten than as long strings of digits. Calculators show big results this way too (often as “3E8”).

Common Conversion Slips

Your Turn: Convert

Convert each (to or from scientific notation), then reveal the answers.

Frequently Asked Questions

Related Topics

Continue Your Study

Ready for the next step? Pick up right where this lesson leaves off: