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
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 digits numbers by positive 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
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
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.
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