# Five Clarifications On Multiply Using Expanded Form Lesson 10.10 Answers | Multiply Using Expanded Form Lesson 10.10 Answers

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Today we’re activity to use the abject ten place-value arrangement to acquire abrogating exponents. So let’s do it!

In a antecedent lesson, I alien the decimal arrangement and exponential notation. Recall the decimal arrangement is abject 10, acceptation we accept 10 syms and we accredit amount to the syms based aloft the attribute and its position.

To acquaint you the truth, this is alone bisected of the story. Don’t worry, algebraic is inherently balanced, so the added bisected of the decimal arrangement is a simple addendum of what we accept above. Let’s acquire it.

Begin by appearance the decimal point to the appropriate of the one’s place. The decimal point separates the accomplished cardinal ethics on the larboard from the apportioned ethics on the right.

Moving left-to-right forth the decimal place-value arrangement is agnate to adding by ten anniversary time. Continue this adding action to the appropriate of the decimal point to access the blow of the decimal system.

We alarm these place-values: tenths, hundredths, thousandths, ten-thousandths, etc.

Place-values on the larboard can be represented in admiral of ten:

Continue the backer arrangement to the appropriate of the decimal point, adding 1 from the backer of anniversary place-value.

We now accept abrogating exponents! How alarming is that?!

Compare the backer representation in diagram 2 to the acceptable representation in diagram 1. What patterns do you notice?

You ability apprehension that the additional and third cavalcade are actual similar. This is an important acumen apropos abrogating exponents.

Negative exponents accurate how abounding times 1 charge be disconnected by the abject number.

Using the place-value assignments, 25.375 is agnate to 2 tens, 5 ones, 3 tenths, 7 hundredths and 5 thousandths. We can accurate this in broadcast anatomy application backer notation.

Or artlessly by the agnate of anniversary place-value.

If we accumulate the articles calm and accomplish the addition, we access aback at the aboriginal value.

At this point you may be wondering:

There is! They are alleged reciprocals or multiplicative inverses because back assorted calm they aftereffect in 1. To demonstrate, we’ll accumulate the afterward two ethics together.

A abrogating backer can be rewritten with an inversion:

Next, aggrandize both exponents and abridge the answer. That proves they are reciprocals of one another.

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