Powers of Ten

Powers of 10

Powers of 10 can be written in two ways:

• With an exponent: 10³

• In expanded form: 1000  (1000 = 10³, note that the number of zeros is equivalent to the exponent)

Powers of 10

 

 

 

 

 

 

 

 

 

Multiplying by a positive power of 10 makes the number larger and multiplying by a negative power of 10 makes the number smaller.

5 x 10¹= 5 x 10 = 50

5 x 10²= 5 x 100 = 500

5 x 10³= 5 x 1,000 = 5,000

5 x 10⁴= 5 x 10,000 = 50,000

To multiply a whole number by a power of ten, just count how many zero you have and attach that to the whole number.

 

MKY3

Multiply By Powers of 10

To divide by a power of 10, simply move the decimal point to the left the same number of places as the exponent or as the number of zeros.  Example:

50 / 10¹= 50/10 = 5

500/10² = 500/100 = 5

5000/10³ = 5000/1000 = 5

Note: The decimal point of a whole number is always to the right of the one’s place.

MKY3

Divide By Powers of 10

Positive, negative and zero exponents with a base of ten

10000 = 1 x 10⁴
1000 = 1 x 10³
100 = 1 x 10²
10 = 1 x 10ᴵ
1 = 10⁰
1/10 = 0.1 = 1 x 10⁻ᴵ
1/100 = 0.01 = 1 x 10⁻²
1/1000 = 0.001 = 1 x 10⁻³
1/10000 = 0.0001 = 1 x 10⁻⁴

When we multiply a number by a positive power of 10, we move the decimal point of the number to the right.

When we multiply a number by a negative power of 10, we move the decimal point of the number to the left.

The number of places to move would be equal to the power of ten.

MKY3

Multiply and divide by positive powers of Ten 1

Multiply and divide by positive powers of Ten 2

Multiply and divide by negative powers of Ten

One-Digit × Positive Powers of Ten

Multiply by 10, 100 or 1000

Multiply a decimal by a power of ten

Multiply a decimal by a power of ten 1

Multiply a decimal by a power of ten 2

Multiply a decimal by a power of ten 3

One-Digit × Multiples of Positive Powers of Ten

Two-Digit × Negative Powers of Ten

Multiply by 0.1, 0.01, and 0.001

One-Digit × Negative Powers of Ten

Two-Digit × Negative Powers of Ten

One-Digit × Multiples of Negative Powers of Ten

Decimals divided by powers of ten

Division by 10, 100, 1000

Division by Factors of ten

Divide decimals by powers of ten 1

Divide decimals by powers of ten 2

Divide decimals by powers of ten 3

Divide a decimal by a power of ten A

Integer ÷ Multiple of Positive Powers of Ten

Integer ÷ Multiple of Negative Powers of Ten

Dividing whole numbers by multiples of 10 (Remainders)

Scientific Notation

Scientific Notation 2

Scientific Notation 3 (Standard Form)

Scientific Notation 4 (Standard Form)