**Powers of 10**

**Powers of 10 can be written in two ways: **

**• With an exponent: 10³**

**• In expanded form: 1000 (1000 = 10³, n****ote 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 zero you have and attach that to the whole number.**

**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.**

**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.

### Whole Numbers Multiplication by 10, 100, 1000

### Dividing Whole Numbers by 10, 100, 1000

### Multiplying Decimals by 10, 100, 1000

### Dividing Decimals by 10, 100, 1000

**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 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**

**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 3 (Standard Form)**

**Scientific Notation 4 (Standard Form)**