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### Course: Staging content lifeboat > Unit 14

Lesson 52: Multiplying and dividing with powers of 10- Exponents and powers of 10 patterns
- Multiplying a decimal by a power of 10
- Dividing a decimal by a power of 10
- Dividing a decimal by a power of 10: pattern
- Multiply and divide by powers of 10
- Understanding moving the decimal
- Fractions as division by power of 10

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# Dividing a decimal by a power of 10: pattern

Discover a pattern when dividing by powers of 10. Created by Sal Khan.

## Want to join the conversation?

- When would you ever have to divide decimals in real life?(8 votes)
- Let's say you had $61.56 and wanted to buy a bunch of candy bars that cost $1.62 apiece. How many could you afford?(62 votes)

- I'm a little bit confused. So, say you had the equation: 0.9* 10 would be 09. or 9.0?

Please help :((1 vote)- I like to think of decimals as money. So 0.9 is 90 cents. What's 90 cents * 10? (or, $0.9 * 10)...well, it can't be 0.09, because that would be 9 cents...why would 10 times 90 cents be 9 cents (which is less than it originally was)? So, 0.9 * 10 must be greater than 90 cents...9.0 or $9.00!

That's an easy way to remember which way you need to move the decimal in these kinds of problems.(6 votes)

- Why do we have to call a decimal a decimal instead of point?(0 votes)
- decimal means something specific. It means a sign in a number that shows the number has parts of a whole number. The word "point", however, means something different in math and geometry. It is a location, a spot on a graph. a way to remember is, a decimal is divided by ten (deci="ten") and a point is a place you can go to.(7 votes)

- What does arbitrary mean?(2 votes)
- based on random choice or personal whim, rather than any reason or system.

"his mealtimes were entirely arbitrary"

synonyms: capricious, whimsical, random, chance, unpredictable; More

(of power or a ruling body) unrestrained and autocratic in the use of authority.

"arbitrary rule by King and bishops has been made impossible"

synonyms: autocratic, dictatorial, autarchic, undemocratic, despotic, tyrannical, authoritarian, high-handed; More

MATHEMATICS

(of a constant or other quantity) of unspecified value.

All of that is the meaning of arbitrary.(2 votes)

- Let's think about this.Can you divide 9.86 by 100's?(2 votes)
- If you mean by 100. Yes, and the answer would be 0.0986.(2 votes)

- So when you divide by 10, the decimal moves to the left and makes the number smaller? And when you're multiplying by 10, it goes to the right?(2 votes)
- Yes, that is correct. 10.0 divide by 10 gives you 1.00, and 10.0 multiplied by 10 gives you 100.(2 votes)

- So basically its just switching the decimal movement depending on what you are doing to the decimal like +, /,-,*(3 votes)
- You said 'arbitrarily' in one sentence, what does that mean?(2 votes)
- Is there any thing the same as the problem i'm on that is accelerated math?(2 votes)
- If not then can you make one like keep making videos of each problem i get to on accelerated math(2 votes)

## Video transcript

In the last video, we divided
100 into 99.061, and we did it the manual way. We did it the long
division way. In this video, I just want to
show you a quick shortcut because we're dividing something
by a power of ten. If I have 99.061, if I multiply
by a power of ten, I'm going to make the
number bigger. Every time I multiply by 10, the
decimal would shift to the right by one spot. So we could say, 99.061
times 10 is going to be equal to 990.61. Notice we just moved
the decimal over to the right by one. If I were to do-- I'll just
arbitrarily switch colors-- 99.061 divided by 10, we're
going to shift the decimal in the other direction. This is going to be 9.9061. So when we divide by 100, we're
dividing by 10 twice. We're shifting to
the left twice. So if we start with 99.061
divided by 100-- let me just write it like this. We've already written
the problem. If we want to divide this by
100, moving it one spot to the left will divide it by 10, and
then moving another spot to the left will divide
it by 10 again. So 99.061 divided by 100 is
going to be equal to 0.99061. We're just going to shift the
decimal to the left by two. And we might want to put a
leading zero here, just so it makes it a little bit
easier to read.