Lesson 2.14

Clearing Decimals

Decimals are just fractions in disguise. Just like we can wipe out fractions with the LCD, we can wipe out decimals by multiplying by 10, 100, or 1000.

Introduction

Solving involves annoying decimal arithmetic. But if we multiply the entire equation by 100, it becomes . Suddenly, it's just a regular integer equation!

Past Knowledge

Multiplying by 10 moves the decimal one spot right. Multiplying by 100 moves it two spots.

Today's Goal

Identify the power of 10 needed to clear all decimals and solve.

Future Success

Essential for chemistry (concentrations) and finance (interest rates).

Key Concepts

Power of 10 Strategy

Look at the number with the MOST decimal places. That determines what you multiply by.

  • 1 Decimal Place (0.5): Multiply all by 10.
  • 2 Decimal Places (0.25): Multiply all by 100.
  • 3 Decimal Places (0.125): Multiply all by 1000.

Worked Examples

Example 1: One Decimal Place

Basic

Solve .

1

Multiply ALL by 10

2

Solve

Example 2: Two Decimal Places

Intermediate

Solve .

1

Identify Max Decimals

0.25 and 0.05 have two places. 0.7 only has one. We must multiply by 100 to clear the worst ones.

2

Multiply ALL by 100

3

Solve

Example 3: Mixed Integers and Decimals

Advanced

Solve .

1

Multiply Entire Equation by 10

Treat the group as one term. Only multiply the coefficient .

2

Distribute and Solve

Common Pitfalls

Missing the Zero

When multiplying 0.7 by 100, many students write "7". It is actually 70. Move the decimal point TWICE, filling empty spots with zeros.

Forgetting Terms

Just like with fractions, you must multply EVERY term. If you have and multiply by 10, the "1" must become "10".

Real-Life Applications

Currency Conversion: Money is a decimal system. If €1 = $1.10, then €x = $330 is . Multiplying by 100 turns it into "cents" (integers): .

Practice Quiz

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