# 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) 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 zeroes you have and attach that to the whole number.

## Multiplying by powers of ten

### PT22      Multiply 2 digits numbers by negative powers of Ten

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.

## Dividing by powers of ten ### PT03      Multiply  and divide by Negative Powers of Ten

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. ### Dividing Decimals by 10, 100, 1000

The same number can be represented in different ways.

The value of the number is the same no matter how it is written.

The Standard Form is the way in which we normally write the numbers using digits.

Scientific notation is a compact way that scientists use to write very large and very small numbers.  The number is expressed in two parts a coefficient (whose absolute value is greater than or equal to 1 but less than 10) multiplied by a power of ten 