Problems that involve metric measurement are good vehicles for developing division by decimals. Although it is reasonable to consider 12 objects measured in lots of 0.6, it is quite a stretch to imagine 12 objects shared into 0.6 equal sets. The questions in this activity use a measurement context for division rather than an equal-sharing context. You need to work with your students to correct this common error of reasoning. As the examples in the chart below illustrate, the opposite is true in many cases. This overgeneralisation is based on what happens with whole numbers. Some may still think that “multiplication makes bigger” and “division makes smaller”. Students must be able to understand multiplication and division by powers of 10 if they are to handle more complex problems. Pages 22–27 of Book 7: Teaching Fractions, Decimals, and Percentages from the NDP resources describe how materials such as deci-mats or decimal pipes can be used to model these patterns in the place value system. Powers of 10 are created by multiplication by 10, so moving one column to the left in the table above equates to division by 10. Students will find it helpful to create this pattern for exponents greater than or equal to 1 and then extend it to the left: Powers of 10 may also be less than 1, but their meaning will be less obvious. Powers of 10 with an exponent of 1 or greater are counting numbers. There are also 3 zeros in the product (1 000). The “3” indicates that 3 tens have been multiplied together. Powers of 10 can be written using exponents, for example, 10 3 = 1 000. Some powers of 10 are:ġ0 x 10 = 100 (ten tens equal one hundred)ġ0 x 10 x 10 = 1 000 (ten times ten times ten equals one thousand)ġ0 x 10 x 10 x 10 = 10 000 (ten times ten times ten times ten equals ten thousand)ġ0 x 10 x 10 x 10 x 10 = 100 000 (ten times ten times ten times ten times ten equals one hundred thousand). Powers of 10Īre created by multiplying tens together. If you found this content useful in your research, please do us a great favor and use the tool below to make sure you properly reference us wherever you use it.The questions in this activity are about multiplication and division by powers of 10. Now that you know what 10 to the 10th power is you can continue on your merry way.įeel free to share this article with a friend if you think it will help them, or continue on down to find some more examples. Hopefully this article has helped you to understand how and why we use exponentiation and given you the answer you were originally looking for. Why do we use exponentiations like 10 10 anyway? Well, it makes it much easier for us to write multiplications and conduct mathematical operations with both large and small numbers when you are working with numbers with a lot of trailing zeroes or a lot of decimal places. Now that we've explained the theory behind this, let's crunch the numbers and figure out what 10 to the 10th power is:ġ0 to the power of 10 = 10 10 = 10,000,000,000 Let's look at that a little more visually:ġ0 to the 10th Power = 10 x. So we mentioned that exponentation means multiplying the base number by itself for the exponent number of times. The caret is useful in situations where you might not want or need to use superscript. So basically, you'll either see the exponent using superscript (to make it smaller and slightly above the base number) or you'll use the caret symbol (^) to signify the exponent. There are a number of ways this can be expressed and the most common ways you'll see 10 to the 10th shown are: The exponent is the number of times to multiply 10 by itself, which in this case is 10 times. When we talk about exponentiation all we really mean is that we are multiplying a number which we call the base (in this case 10) by itself a certain number of times. Let's get our terms nailed down first and then we can see how to work out what 10 to the 10th power is. That might sound fancy, but we'll explain this with no jargon! Let's do it. So you want to know what 10 to the 10th power is do you? In this article we'll explain exactly how to perform the mathematical operation called "the exponentiation of 10 to the power of 10".
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