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 zeroes you have and attach that to the whole number.

PT06      Multiply_by_10_100_1000

PT07      Multiply by 0.1, 0.01, and 0.001

PT27      Multiply One-Digit × Multiples of Positive Powers of Ten

PT05      Multiply a decimal by a power of ten

PT08      Multiply a decimal number by a power of Ten 1

PT09      Multiply a decimal number by a power of Ten 2

PT10      Multiply a decimal by a power of Ten 3

PT11      Multiply a decimal by a power of Ten 4

PT12      Multiply a decimal by a power of Ten 5

PT13      Multiply a decimal by a power of Ten 6

PT21      Multiply 1 digit by positive powers of Ten

PT25      Multiply One-Digit × Multiples of Negative Powers of Ten

PT28      Multiply One-Digit × Multiples of Negative Powers of Ten

PT23      Multiply 2 digit by positive powers of Ten

PT22      Multiply 2 digits 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.

 

PT14      Divide_by_powers of Ten 1

PT15      Divide_a decimal by 10_100_1000

PT16      Divide_ a decimal by a power of Ten 3

PT17      Divide_Decimal by powers of Ten 4

PT18      Divide a decimal by powers of Ten 5

PT19      Divide_a decimal by powers of ten 6

PT20      Divide_ a decimal by a power of Ten 7

PT24      Divide an integer ÷ Multiples of Negative Powers of Ten

PT26      Divide an Integer ÷ Multiples of Positive Powers of Ten

 

PT01      Multiply and divide by positive powers of_Ten 1

PT02      Multiply  and divide by positive powers of Ten 2

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.

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

 

PT04      Write Powers of Ten

 

DE08      Scientific Notation 1

DE10      Scientific_Notation 2

DE02      Converting to Standard_Form 1

DE03      Converting to Standard_Form_2