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, 100 = 1, 101 = 10, 102 = 100, 103 = 1000.
Most Popular Powers of Ten Worksheets this Week
Learning 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. This allows students to see patterns in multiplying or dividing by a set of powers of ten.
A good place to start is with the powers of ten in standard form. Later on, introduce students to the exponent form as they will already know how to multiply or divide with powers of ten and can focus on learning the relationship between the exponents and the number of zeros they need to work with.
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Numbers from 1 to 10 × Positive Powers of Ten (Standard Form) Two-Digit Numbers × Positive Powers of Ten (Standard Form) Numbers from 1 to 10 × Negative Powers of Ten (Standard Form) Two-Digit Numbers × Negative Powers of Ten (Standard Form) Whole Number × Negative Powers of Ten (Whole Number Results) (Standard Form)
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Numbers from 1 to 10 × Positive Powers of Ten (Exponent Form) Two-Digit Numbers × Positive Powers of Ten (Exponent Form) Numbers from 1 to 10 × Negative Powers of Ten (Exponent Form) Two-Digit Numbers × Negative Powers of Ten (Exponent Form) Numbers from 1 to 10 × Negative Powers of Ten (Whole Number Results) (Exponent Form)
Multiplying with multiples of powers of ten has tremendous benefits in mental math. Think about long multiplication which is essentially multiplying by multiples of powers of ten. For example, 456 × 4 can be thought of as 4 × 400 + 4 × 50 + 4 × 6. The more comfortable students are with handling all those extra zeros, the less often they will make mistakes.
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Numbers from 1 to 10 × Multiples of Positive Powers of Ten (Standard Form) Two-Digit Numbers × Multiples of Positive Powers of Ten (Standard Form) Numbers from 1 to 10 × Multiples of Negative Powers of Ten (Standard Form) Two-Digit Numbers × Multiples of Negative Powers of Ten (Standard Form) Whole Number × Multiples of Negative Powers of Ten (Whole Number Results) (Standard Form)
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Numbers from 1 to 10 × Multiples of Positive Powers of Ten (Exponent Form) Two-Digit Numbers × Multiples of Positive Powers of Ten (Exponent Form) Numbers from 1 to 10 × Multiples of Negative Powers of Ten (Exponent Form) Two-Digit Numbers × Multiples of Negative Powers of Ten (Exponent Form) Numbers from 1 to 10 × Multiples of Negative Powers of Ten (Whole Number Results) (Exponent Form)
The learning to divide by powers of ten worksheets include the same number divided by the positive or negative powers of ten.
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Numbers from 1 to 10 ÷ Positive Powers of Ten (Standard Form) Two-Digit Numbers ÷ Positive Powers of Ten (Standard Form) Numbers from 1 to 10 ÷ Negative Powers of Ten (Standard Form) Two-Digit Numbers ÷ Negative Powers of Ten (Standard Form) Whole Number ÷ Positive Powers of Ten (Whole Number Results)
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Numbers from 1 to 10 ÷ Positive Powers of Ten (Exponent Form) Two-Digit Numbers ÷ Positive Powers of Ten (Exponent Form) Numbers from 1 to 10 ÷ Negative Powers of Ten (Exponent Form) Two-Digit Numbers ÷ Negative Powers of Ten (Exponent Form) Numbers from 1 to 10 ÷ Positive Powers of Ten (Whole Number Results) (Exponent Form)
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Numbers ÷ Multiples of Positive Powers of Ten (Standard Form) (Quotients 1 to 10) Numbers ÷ Multiples of Positive Powers of Ten (Standard Form) (Quotients 10 to 99) Numbers ÷ Multiples of Negative Powers of Ten (Standard Form) (Quotients 1 to 10) Numbers ÷ Multiples of Negative Powers of Ten (Standard Form) (Quotients 10 to 99) Whole Number ÷ Multiples of Positive Powers of Ten (Whole Number Results)
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Numbers from 1 to 10 ÷ Multiples of Positive Powers of Ten (Exponent Form) Two-Digit Numbers ÷ Multiples of Positive Powers of Ten (Exponent Form) Numbers from 1 to 10 ÷ Multiples of Negative Powers of Ten (Exponent Form) Two-Digit Numbers ÷ Multiples of Negative Powers of Ten (Exponent Form) Numbers from 1 to 10 ÷ Multiples of Positive Powers of Ten (Whole Number Results) (Exponent Form)
Multiplying and Dividing Whole Numbers by Powers of Ten
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 100 is the same as multiplying by 1.
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 100 is the same as dividing by 1.
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.
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Whole Number × or ÷ All Powers of Ten (Standard Form) Whole Number × or ÷ All Positive Powers of Ten (Standard Form) Whole Number × or ÷ All Negative Powers of Ten (Standard Form) Whole Number × or ÷ 0.001 Whole Number × or ÷ 0.01 Whole Number × or ÷ 0.1 Whole Number × or ÷ 10 Whole Number × or ÷ 100 Whole Number × or ÷ 1,000
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Whole Number × or ÷ All Powers of Ten (Exponent Form) Whole Number × or ÷ All Positive Powers of Ten (Exponent Form) Whole Number × or ÷ All Negative Powers of Ten (Exponent Form) Whole Number × or ÷ 10-3 Whole Number × or ÷ 10-2 Whole Number × or ÷ 10-1 Whole Number × or ÷ 101 Whole Number × or ÷ 102 Whole Number × or ÷ 103
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Whole Number × or : All Powers of Ten (Standard Form) Whole Number × or : All Positive Powers of Ten (Standard Form) Whole Number × or : All Negative Powers of Ten (Standard Form) Whole Number × or : 0,001 Whole Number × or : 0,01 Whole Number × or : 0,1 Whole Number × or : 10 Whole Number × or : 100 Whole Number × or : 1.000
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Whole Number × or : All Powers of Ten (Exponent Form) Whole Number × or : All Positive Powers of Ten (Exponent Form) Whole Number × or : All Negative Powers of Ten (Exponent Form) Whole Number × or : 10-3 Whole Number × or : 10-2 Whole Number × or : 10-1 Whole Number × or : 101 Whole Number × or : 102 Whole Number × or : 103
Multiplying and Dividing Decimals by Powers of Ten
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....
