Expanded form with powers of 10

The idea

A number, including a decimal, is written in expanded form as each digit times a power of 10, with 10⁰ for the units place and 10⁻¹, 10⁻², 10⁻³, … for the decimal places.

The units place

47561 = (4 × 10000) + (7 × 1000) + (5 × 100) + (6 × 10) + 1

Each place value is a power of 10: 10000 = 10^4, 1000 = 10^3, 100 = 10^2, 10 = 10^1.

What power of 10 is the units place (the last digit 1)?

• 10^1
• 10^0
• 0

Build the number

Each column has a power of 10. Press ▲ and ▼ to set the digits. Make the numbers.

Each digit times a power of 10

A number, including a decimal, is written in expanded form as each digit times a power of 10, with 10⁰ for the units place and 10⁻¹, 10⁻², 10⁻³, … for the decimal places.

47561 = (4 × 10^4) + (7 × 10^3) + (5 × 10^2) + (6 × 10^1) + (1 × 10^0)

561.903 = (5 × 10^2) + (6 × 10^1) + (1 × 10^0) + (9 × 10⁻¹) + (0 × 10⁻²) + (3 × 10⁻³)

Because 10⁻¹ = 1/10, 10⁻² = 1/100 and 10⁻³ = 1/1000.

Notes

A number is written in expanded form as each digit times a power of 10: 10⁰ for units, 10⁻¹, 10⁻², 10⁻³, … for the decimal places.

Check yourself

In 561.903, the digit 9 sits in the place with value:

(3 × 10^2) + (5 × 10^1) + (7 × 10^0) is which number?

Answer: 357

300 + 50 + 7 = 357.

In 561.903, which digit is multiplied by 10⁻³?

Answer: 3

The places after the point are 9 → 10⁻¹, 0 → 10⁻², 3 → 10⁻³.

In 0.25 = (2 × 10⁻¹) + (5 × …), the 5 is multiplied by 10 raised to which power? (Type the exponent.)

Answer: -2

The 5 is in the second place after the point, which is 10⁻² (hundredths).

• 10¹. 10¹ is the tens place (the 6). The 9 is after the decimal point.
• 10⁻¹ — correct. Yes! The first place after the decimal point is 10⁻¹ = 1/10.
• 10⁻². 10⁻² is the next place, the 0. The 9 comes first after the point.