In this lesson, students will learn how to convert between scientific notation and standard form. They’ll start with an introduction which reviews what they already know about exponents. We’ll expand that to help convert scientific notation to standard form, then the other way around. You can expect this lesson to take one `45`-minute class period.
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Students will be able to convert numbers in standard form to scientific notation.
Students will be able to convert numbers in scientific notation to standard form.
Start off the class by showing slide `1` in the slideshow. Your students will already be familiar with the concept of positive and negative exponents. The key here is that we’re bringing in a base of `10` to have students easily transition into scientific notation.
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Allow students a few minutes to come up with answers independently, then share with the class. Here are some answers you might expect.
You’ll want to focus in on what these exponential expressions simplify to. Students should understand that the positive exponent will give us a number greater than `1` and the negative exponent will give us a number less than `1`.
Take this first example step by step by using the transitions on the slide. Since you just simplified `10^3` in the warm up, ask students again what it simplified to. Then students just need to multiply `5` by `1,000` to see that `5 \cdot 10^3` is `5,000`.
Take this opportunity to show students that since we’re multiplying by powers of `10`, we can use place value to get to the answer more quickly. Start by asking students, “since the power of `10` we’re multiplying by has a positive exponent, which direction should we move the decimal?” The key is for students to recognize that a positive exponent will make the coefficient larger, so we need to move the decimal point to the right.
This next example has a negative exponent. You’ll want to carry over the thinking from the previous problem with moving the decimal point. Ask students, “since the power of `10` has a negative exponent, which direction do you think we’ll move the decimal point in `8.2`?” The key is for students to recognize that this would make `8.2` smaller, so we need to move the decimal to the left.
Typically, it’s easier for students to convert from scientific notation to standard form, since they’re really just multiplying! So up until this point, we haven’t pointed out what the key ideas are behind scientific notation. Show the next slide and point out the key points while they write this in their notebooks.
You’ll want to highlight the following ideas:
For the next slide, let students work together to determine whether each value is written in scientific notation or not. Once students are done, go over each one as a class. Ask for volunteers to come up to the board to explain whether the value is written in scientific notation or not and if not, why not!
Now we’ll want to convert a number in standard form into scientific notation. I like to start by asking students where the decimal point would be and drawing that in. Then, tell students we’re going to move the decimal point until it’s in a place where the number would be between `1` and `10`. So in this case, we’ll move the decimal point `4` places to the left, making the coefficient `4.5`.
Next is determining the exponent. I try not to focus on “rules” like “moving left means the exponent is positive” because this confuses students when converting back and forth. Rather, I ask students to think about if the value of the number is greater than the coefficient. Since `45,000` is a large number it is definitely greater than `4.5`, so we should write a positive exponent. Since we moved the decimal point `4` times, the exponent will be positive `4`.
Follow a similar process with this example. Start moving the decimal point until the number is between `1` and `10`. Then, determine if the exponent will be positive or negative. Since `0.0000821` is smaller than `8.21`, we’ll write a positive exponent. Since we move the decimal `5` times, the exponent will be positive `5`.
Now it’s time for some independent practice! You can assign a ByteLearn online practice to your class using the link below. Students will get immediate feedback and step-by-step help if they need it. Set a due date and allow students to finish the assignment for homework. Once complete, you’ll see detailed reports of students who may need additional support, students who are ready for a challenge, and other interesting insights!
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