Understanding Place Value and Powers

Year 7 Mathematics Mastering Powers of 10 - Lesson 1 Duration: 60 minutes

Digit Detective Starter

Look at this number: 3,482,905.276 Find the digit in the hundred thousands place What is the value of the digit 7? Which digit is in the hundredths place?

What is Place Value?

Each digit in a number has a specific position The position determines the digit's value Moving left increases value by 10 times Moving right decreases value by 10 times The decimal point separates whole numbers from parts

Place Value Chart: Millions to Thousandths

Powers of 10

Powers of 10 are numbers like 10, 100, 1000, 10000 Multiplying by 10¹ moves digits one place left Dividing by 10² moves digits two places right Example: 45 × 100 = 4500 (digits shift left) Example: 3600 ÷ 1000 = 3.6 (digits shift right)

Expanded Form

Shows the value of each digit separately Example: 345.678 = 3×100 + 4×10 + 5×1 + 6×0.1 + 7×0.01 + 8×0.001 Helps us see the true value of each digit

Quick Check

What is the value of the digit 8 in each number? A) 2,847 B) 18.39 C) 450.082

Hands-On Place Value

Work in groups of 6 Use digit cards and place value charts Build numbers and identify digit values Move digits to show ×10 and ÷10 effects

Key Takeaway

Place value is the foundation of our number system. Understanding how digits change value when they move positions prepares us to work confidently with powers of 10.

Powers of 10 Practice Challenge

Convert 3.2 × 10³ to standard form Write 0.0045 in scientific notation Calculate 2.5 × 10² + 1.8 × 10² Express 56,000 using powers of 10 Find the value of 4.7 × 10⁻²

Key Vocabulary: Place Value & Powers of 10

Place Value: The value of a digit based on its position Digit: Any number from 0 to 9 Powers of 10: Numbers like 10, 100, 1000 (10 × 10 × 10...) Standard Form: Writing numbers normally (e.g., 3,456) Expanded Form: Breaking down by place value (3000 + 400 + 50 + 6) Decimal Place: Positions after the decimal point (tenths, hundredths)