Free Interactive Pre-Algebra Tool

Scientific Notation

Learn how powers of ten move the decimal, convert numbers in both directions, and explain what positive and negative exponents mean.

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Learn Why the Decimal Moves

Review coefficients, powers of ten, positive and negative exponents, decimal movement, and worked conversions.

Read the Scientific Notation Guide

How It Works

Make Every Decimal Move Mean Something

Scientific notation writes a number as a coefficient from 1 up to 10 multiplied by a power of ten. Each decimal place moved changes the exponent by one.

1

Choose a Direction

Decide whether the decimal must move left or right for the conversion you are making.

2

Count Every Place

The number of places moved becomes the size of the exponent on 10.

3

Use the Correct Sign

Large standard numbers use positive exponents; small decimals use negative exponents.

4

Check the Coefficient

A scientific-notation coefficient must be at least 1 but less than 10.

Interactive Practice

Convert One Step at a Time

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Problems 0
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Write in Scientific Notation

Medium

Move the decimal until the coefficient is at least 1 but less than 10.

48,200
The direction and distance of the decimal move determine the exponent.
  1. 1 Direction
  2. 2 Places
  3. 3 Convert
  4. 4 Explain
1

Plan the Move

Which Way Does the Decimal Move?

Current Step

Current Problem

Medium

Move the decimal until the coefficient is at least 1 but less than 10.

48,200
The direction and distance of the decimal move determine the exponent.

Choose the direction that creates a coefficient between 1 and 10.

2

Measure the Move

How Many Places Does It Move?

Locked

Current Problem

Medium

Move the decimal until the coefficient is at least 1 but less than 10.

48,200
The direction and distance of the decimal move determine the exponent.

Complete Step 1 to unlock the place count.

3

Write the Result

Complete the Conversion

Locked

Current Problem

Medium

Move the decimal until the coefficient is at least 1 but less than 10.

48,200
The direction and distance of the decimal move determine the exponent.

Complete Step 2 to unlock the final conversion.

Keep This Nearby

Scientific Notation Reference

The coefficient is at least 1 and less than 10. The exponent records decimal places.

Large Number Move left → positive exponent 45,000 = 4.5 × 104
Small Decimal Move right → negative exponent 0.0062 = 6.2 × 10−3
Positive Power Move right to return to standard form 3.7 × 105 = 370,000
Negative Power Move left to return to standard form 8.1 × 10−4 = 0.00081

Key Reminders

Avoid the Most Common Conversion Mistakes

Check these three details before submitting an answer.

Keep One Nonzero Digit in Front

The coefficient must be at least 1 but less than 10.

6.2 × 104, not 62 × 103

Count Places, Not Zeros

Count every position the decimal crosses, including positions occupied by nonzero digits.

381,000 → 3.81 moves 5 places

Match Direction and Sign

Moving left to make a coefficient gives a positive exponent; moving right gives a negative exponent.

0.00072 = 7.2 × 10−4

Preserve Every Significant Digit

Moving the decimal changes place value, not the order of the digits.

50,600 = 5.06 × 104

Keep Learning

Understand the Power of Ten Behind Every Move

Review coefficients, powers of ten, decimal movement, exponent signs, and fully worked conversions in the complete guide.

Read the Scientific Notation Guide