Decimal Division and Multiplication

Concept

  • Value of 1 (tenth), 2 (hundredth) and 3 (thousandth) decimal places.
  • Multiply a decimal with 10, 100, 1000.
  • Divide a decimal with 10, 100, 1000.

Theory

Decimal place values

Sometimes having numbers till just the units is not enough. Let’s say you go to buy gold. That metal is so expensive even 1g of it is going set you back by a small fortune. So we come up the concept of decimals.

0.1 grams.

Now that’s 1/tenth of a gram, and so ten times cheaper too (mathematically speaking!). You could buy 1/10th, of 0.1 grams of gold without breaking the bank.

What about if you want to buy Rhodium? That stuff is even more expensive than gold, so you can probably only afford a smaller quantity only. Like a hundredth of a gram.

0.01 grams

0.01 grams, is all you could buy. It would cost you almost twenty thousand rupees!

Finally, what if you wanted to buy krypton from Superman? Superman’s been known to drive a hard bargain, so he can offer you just a thousandth of a gram of Kryptonite for a gadzillion bucks.

0.001 grams.

That’s tiny. But hold on to it. You paid a lot of money for it.

Remember that 0.1 > 0.01 > 0.001.

So here is nice decimal number in all it’s “up to 3 decimal places” glory.

Multiply/divide by 10, 100, 1000
  • To multiply, count the number of zeros and move the decimal that many places to the left.
  • To multiply, count the number of zeros and move the decimal that many places to the right.
  • If you run out places when moving place, add 0s.

Notice:

  • 3.012 x 1000 = 3012
  • 3.012 x 10000 = 30120 (add 0)
  • 3.012 / 10 = .3012
  • 3.012 / 100 = .03012 (add 0)
Multiply two decimals

What about if you have to multiply 3.2 x 2.6.

  • Multiply as if the decimals did not exist. So multiply 32 x 26. That is equal to 832
  • How many decimal points are there in original question? Two.
  • Add two decimals from the right
  • Answer is 8.32
Divide two whole numbers to 2 decimal places

Let’s say you have to divide 762/24, but instead of leaving out the remainder, you have to keep going into the “decimal land!”

  • Remember - for every decimal, you can add a zero to the remainder.
Divide a decimal by a whole number

So here is how you would divide, say 64.48 by 16.

Divide a decimal by another decimal number

The first step is to make the divisor a whole number. In the expression 76.2 / 2.4, the divisor is 2.4.

  • To make the divisor a whole number, multiply both the numerator and the denominator by 10.
  • Now we have 762/24.
  • Now start the division as before

Trailing zeroes.

Decimal division wrapped in a word problem. Watch out for the word “more.”

Common Misconceptions

  • Reporting out the value based on the value of the digit instead of its place value
    • In 2.29, .2 is greater than .09.
  • Getting confused when you have to move more places than you have digits
    • Add 0s as appropriate.

Quiz

Test your concept

https://quizizz.com/embed/quiz/640f3e9fb823dc001df3eee8 (Decimal multiplication) https://quizizz.com/embed/quiz/640f41ae503cc3001d61930d (Decimal division)