1.7 Decimals  (Page 4/10)

To divide decimals, determine what power of 10 to multiply the denominator by to make it a whole number. Then multiply the numerator by that same power of $10.$ Because of the equivalent fractions property, we haven’t changed the value of the fraction! The effect is to move the decimal points in the numerator and denominator the same number of places to the right. For example:

We use the rules for dividing positive and negative numbers with decimals, too. When dividing signed decimals, first determine the sign of the quotient and then divide as if the numbers were both positive. Finally, write the quotient with the appropriate sign.

We review the notation and vocabulary for division:

We’ll write the steps to take when dividing decimals, for easy reference.

Divide: $\mathrm{-25.56}÷\left(\mathrm{-0.06}\right).$

Solution

Remember, you can “move” the decimals in the divisor and dividend because of the Equivalent Fractions Property.

	$\mathrm{-25.65}÷\left(\mathrm{-0.06}\right)$
The signs are the same.	The quotient is positive.
Make the divisor a whole number by “moving” the decimal point all the way to the right.
“Move” the decimal point in the dividend the same number of places.
Divide. Place the decimal point in the quotient above the decimal point in the dividend.
Write the quotient with the appropriate sign.	$\mathrm{-25.65}÷\left(\mathrm{-0.06}\right)=427.5$

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A common application of dividing whole numbers into decimals is when we want to find the price of one item that is sold as part of a multi-pack. For example, suppose a case of 24 water bottles costs $3.99. To find the price of one water bottle, we would divide $3.99 by 24. We show this division in [link] . In calculations with money, we will round the answer to the nearest cent (hundredth).

Divide: $\mathrm{\$3.99}÷24.$

Solution

	$\mathrm{\$3.99}÷24$
Place the decimal point in the quotient above the decimal point in the dividend.
Divide as usual. When do we stop? Since this division involves money, we round it to the nearest cent (hundredth.) To do this, we must carry the division to the thousandths place.
Round to the nearest cent.	$\mathrm{\$0.166}\approx \mathrm{\$0.17}$ $\mathrm{\$3.99}÷24\approx \mathrm{\$0.17}$

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Convert decimals, fractions, and percents

We convert decimals into fractions by identifying the place value of the last (farthest right) digit. In the decimal 0.03 the 3 is in the hundredths place, so 100 is the denominator of the fraction equivalent to 0.03.

Notice, when the number to the left of the decimal is zero, we get a fraction whose numerator is less than its denominator. Fractions like this are called proper fractions .

The steps to take to convert a decimal to a fraction are summarized in the procedure box.