Dividing decimals by decimals

When dividing decimals by decimals, such as 45.89 ÷ 0.006, we are told to move the decimal point in both the dividend and the divisor so many steps that the divisor becomes a whole number. Then, you use long division. But why?

Schoolbooks often don't tell us the "why", just the "how".

This video explores this concept.


Divide decimals - why do we move the decimal point?


It has to do with the fact that when we move the decimal point, we are multiplying both numbers by 10, 100, 1000, or some other power of ten. When the dividend and the divisor are multiplied by the same number, the quotient does not change. This principle makes sense:

0.344 ÷ 0.004 can be thought of, "How many times does four thousandths fit into 344 thousandths?"

The same number of times as what four fits into 344!

So, 0.344 ÷ 0.004 can be changed into the division problem 344 ÷ 4 without changing the answer. Both 0.344 and 0.004 got multiplied by 1000.

When we simplify fractions or write equivalent fractions, we use the same principle. Remember, fractions are like division problems.

3/7 is 3 ÷ 7.

And, 3/7 = 6/14. We can multiply the numerator and the denominator (or the dividend and the divisor) by some same number, without changing the value of the fraction (the quotient).

Or, 90/100 = 9/10. Or 0.9/0.2 = 9/2.

Exponent worksheets

There's a new addition at HomeschoolMath.net, free exponent worksheets.

You can create an unlimited supply of free printable exponents worksheets there. The worksheets concentrate on calculations with exponents, such as solving 3³ or (1/2)⁴ or (-5)⁰ or 8^-2. You can choose to include negative or zero exponent. You can choose fractions, decimals, or negative numbers as bases. You can also make worksheets that have one other operation besides exponentiation (several operations with powers).

World Math Day 2010

World Math Day 2010 is coming up on March 3rd. You might remember it from last year. It is a free event and lots of fun for the kids.

Registrations close March 2nd. Once you register, you can go practice at the website.

In it, students complete against other students from around the globe in REAL time, with simple mental math questions (such as 7 + 8 or 24 ÷ 4 or 9 × 9). It involves more than 2 million students from over 200 countries.

• Brand NEW format.
• Be part of setting a world record!
• Designed for all ages and ability levels. Simple to register and participate. All you need is Internet access.
• Great prizes
• And it’s absolutely free!!

Remember to hurry because the registration closes March 2nd, 2010.

www.worldmathday.com