Topic 4

Powers of 10 & place value

Powers of 10 name places in a number. 10² = 100, 10⁰ = 1, and 10⁻² = 0.01. The exponent tells you the place.

Class slides 47–52

Find the digit's place: hundreds, tens, ones, tenths, hundredths, and so on.
Match that place to a power of 10. Places right of the decimal use negative exponents.
For expanded form, multiply each nonzero digit by its place value and add.

Expand 4,207.03:

4 × 10³ + 2 × 10² + 7 × 10⁰ + 3 × 10⁻²

That is 4,000 + 200 + 7 + 0.03.

Draw a place-value chart from thousands to thousandths. Fill in 10³, 10², 10¹, 10⁰, 10⁻¹, 10⁻², 10⁻³.

Watch out: 0.002 is 2 × 10⁻³. It is not a single power of 10.

Try it:

Write 0.01 as a power of 10. Then write 0.002 using a digit times a power of 10.

I can do this

Show answer

0.01 = 10⁻², and 0.002 = 2 × 10⁻³.

Try all three before you open the solutions.

Warm-up

What are 10³ and 10⁻³ as ordinary numbers?

Show solution

10³ = 10 × 10 × 10 = 1000. 10⁻³ = 1 ÷ 1000 = 0.001.

Practice

Write 0.007 as a digit times a power of 10.

Show solution

The 7 is in the thousandths place. Therefore 0.007 = 7 × 10⁻³.

Challenge

Write 3,405.2 in expanded form using powers of 10.

Show solution

3,405.2 = 3 × 10³ + 4 × 10² + 5 × 10⁰ + 2 × 10⁻¹. The missing tens digit is 0, so that term can be left out.