Welcome to the powers of ten math worksheets page at Math-Drills.com where you have the power to learn this important skill! This page includes Powers of ten math worksheets with whole numbers and decimals in comma/point and point/comma formats for students to learn this important skill.

Understanding how to multiply and divide by powers of ten is one of those essential skills that students can't do without. It makes it easier to use estimation skills, it is essential in learning large and small numbers, and solidifies an understanding of place value and numbers in general. This page includes a lot of powers of ten worksheets with whole numbers on them because there are fewer digits to work with and the decimal place is in a consistent location which means that the whole number worksheets will prove to be a nice stepping stone to the more difficult decimal versions further down the page.

Positive powers of ten refers to 10, 100, and 1,000. Negative powers of ten refers to 0.1, 0.01, and 0.001. We've supplied worksheets in both standard form and exponent form. In case this is new to you, 10^{-3} = 0.001, 10^{-2} = 0.01, 10^{-1} = 0.1, 10^{0} = 1, 10^{1} = 10, 10^{2} = 100, 10^{3} = 1000.

Worksheets for learning the patterns associated with multiplying and dividing by powers of ten.

The learning to multiply by powers of ten worksheets include the same number multiplied by the positive or negative powers of ten. The powers of ten are currently in the standard/decimal form only.

One-Digit × Multiples of Positive Powers of Ten (Whole Number Products)
Two-Digit × Multiples of Positive Powers of Ten (Whole Number Products)
One-Digit × Multiples of Negative Powers of Ten (Decimal Products)
Two-Digit × Multiples of Negative Powers of Ten (Decimal Products)
Whole Number × Multiples of Negative Powers of Ten (Whole Number Products)

The learning to divide by powers of ten worksheets include the same number divided by the positive or negative powers of ten. The powers of ten are currently in the standard/decimal form only.

One-Digit ÷ Multiples of Positive Powers of Ten (Decimal Quotient)
Two-Digit ÷ Multiples of Positive Powers of Ten (Decimal Quotient)
Whole Number ÷ Multiples of Positive Powers of Ten (Whole Number Quotient)
One-Digit ÷ Multiples of Negative Powers of Ten
Two-Digit ÷ Multiples of Negative Powers of Ten

Worksheets to practice multiplying and dividing whole numbers by powers of ten with mixed and individual powers of ten and both standard and exponent forms.

Multiplying by positive powers of ten always makes a number larger in absolute value. Conversely, multiplying by negative powers of ten always makes a number smaller in absolute value. Multiplying by 10^{0} is the same as multiplying by 1.

Whole Number × All Powers of Ten (Standard Form)
Whole Number × All Powers of Ten (Exponent Form)
Whole Number × All Positive Powers of Ten (Standard Form)
Whole Number × All Positive Powers of Ten (Exponent Form)
Whole Number × All Negative Powers of Ten (Standard Form)
Whole Number × All Negative Powers of Ten (Exponent Form)

Whole Number × All Powers of Ten (Standard Form)
Whole Number × All Powers of Ten (Exponent Form)
Whole Number × All Positive Powers of Ten (Standard Form)
Whole Number × All Positive Powers of Ten (Exponent Form)
Whole Number × All Negative Powers of Ten (Standard Form)
Whole Number × All Negative Powers of Ten (Exponent Form)

Dividing by positive powers of ten always makes a number smaller in absolute value. Conversely, dividing by negative powers of ten always makes a number larger in absolute value. Dividing by 10^{0} is the same as dividing by 1.

Whole Number ÷ All Powers of Ten (Standard Form)
Whole Number ÷ All Powers of Ten (Exponent Form)
Whole Number ÷ All Positive Powers of Ten (Standard Form)
Whole Number ÷ All Positive Powers of Ten (Exponent Form)
Whole Number ÷ All Negative Powers of Ten (Standard Form)
Whole Number ÷ All Negative Powers of Ten (Exponent Form)

Whole Number : All Powers of Ten (Standard Form)
Whole Number : All Powers of Ten (Exponent Form)
Whole Number : All Positive Powers of Ten (Standard Form)
Whole Number : All Positive Powers of Ten (Exponent Form)
Whole Number : All Negative Powers of Ten (Standard Form)
Whole Number : All Negative Powers of Ten (Exponent Form)

These math worksheets should help to mix things up a bit. Mixing up operations on a page helps students pay attention to detail and challenges them to access more processes while they complete the questions. The first worksheets below include all of the powers of ten from 0.001 to 1,000. If students are able to ace these first worksheets, it is probably time to move onto the more challenging decimal worksheets further down this page.

Whole Number × or ÷ All Powers of Ten (Standard Form)
Whole Number × or ÷ All Powers of Ten (Exponent Form)
Whole Number × or ÷ All Positive Powers of Ten (Standard Form)
Whole Number × or ÷ All Positive Powers of Ten (Exponent Form)
Whole Number × or ÷ All Negative Powers of Ten (Standard Form)
Whole Number × or ÷ All Negative Powers of Ten (Exponent Form)

Whole Number × or ÷ 0.001
Whole Number × or ÷ 10^{-3}
Whole Number × or ÷ 0.01
Whole Number × or ÷ 10^{-2}
Whole Number × or ÷ 0.1
Whole Number × or ÷ 10^{-1}
Whole Number × or ÷ 10
Whole Number × or ÷ 10^{1}
Whole Number × or ÷ 100
Whole Number × or ÷ 10^{2}
Whole Number × or ÷ 1,000
Whole Number × or ÷ 10^{3}

Whole Number × or : All Powers of Ten (Standard Form)
Whole Number × or : All Powers of Ten (Exponent Form)
Whole Number × or : All Positive Powers of Ten (Standard Form)
Whole Number × or : All Positive Powers of Ten (Exponent Form)
Whole Number × or : All Negative Powers of Ten (Standard Form)
Whole Number × or : All Negative Powers of Ten (Exponent Form)

Whole Number × or : 0,001
Whole Number × or : 10^{-3}
Whole Number × or : 0,01
Whole Number × or : 10^{-2}
Whole Number × or : 0,1
Whole Number × or : 10^{-1}
Whole Number × or : 10
Whole Number × or : 10^{1}
Whole Number × or : 100
Whole Number × or : 10^{2}
Whole Number × or : 1.000
Whole Number × or : 10^{3}

Worksheets to practice multiplying and dividing decimal numbers by powers of ten with mixed and individual powers of ten and both standard and exponent forms.

Unlike the whole number worksheets above, these worksheets and the dividing and mixed versions that follow include more digits, more need to know place value and consequently, more of a challenge. This is probably not a good place to start if your students are just learning how to multiply and divide by powers of ten. Instead, try the whole number worksheets further up the page. If they are ready, these worksheets should prove to be a fine challenge and will go a long way in helping your students to be successful in their mathematics learning.

It sometimes takes a little time for students to wrap their heads around dividing by powers of ten, especially by negative powers of ten. This is because students are usually taught that dividing makes a number smaller, but when dividing by negative powers of ten, the result is a larger number. Of course, this only applies to numbers that were positive to begin with....

Decimal × or ÷ All Powers of Ten (Standard Form)
Decimal × or ÷ All Powers of Ten (Exponent Form)
Decimal × or ÷ All Positive Powers of Ten (Standard Form)
Decimal × or ÷ All Positive Powers of Ten (Exponent Form)
Decimal × or ÷ All Negative Powers of Ten (Standard Form)
Decimal × or ÷ All Negative Powers of Ten (Exponent Form)

Decimal × or : All Powers of Ten (Standard Form)
Decimal × or : All Powers of Ten (Exponent Form)
Decimal × or : All Positive Powers of Ten (Standard Form)
Decimal × or : All Positive Powers of Ten (Exponent Form)
Decimal × or : All Negative Powers of Ten (Standard Form)
Decimal × or : All Negative Powers of Ten (Exponent Form)