Decimal Numbers
To multiply and divide decimal numbers, you multiply as if they were whole numbers. After
that, the only question is: Where do you put the decimal point?!
Multiplication: Whole Number and Decimal
Example:
4.36 × 4 = ?
Solution:
First we need to find the total weight.
Multiply the average weight by the number of birds, as if it were a whole
number.
multiplicand
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multiplier
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product
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Now, where does the decimal go?
First method for placing decimal point: Estimate!
4 × 4 = 16, so the answer must be a little bigger than 16, that is 17.44.
Estimation is reliable and safe, and keeps you in charge throughout the problem!
Estimation also helps you check your answer.
Second method for placing decimal point: Count the number of positions after the decimal
points, and cut that many off the answer. The number 4.36 has two positions to the right of the
decimal, and the number 4 has none. So cut two positions off from 1744 to get: 17.44
Rounding Decimals
To round a number to a particular place value, locate the digit to be rounded.
Suppose we are to round these numbers to the nearest tenth:
If the digit to the right is 0, 1, 2, 3 or 4, the digit we are rounding stays the same. Drop all the
digits to the right.
If the digit to the right is 5, 6, 7, 8 or 9, the digit we are rounding is raised by one. Drop all the
digits to the right.
Example:
42.71 rounded to the nearest tenth is 42.7
32.481 rounded to the nearest tenth is 32.5
Dividing a Decimal by a Whole Number
Example:
Divide a decimal by whole number:
Divide 20.46 by 66
 .
Note! Put the decimal point in quotient directly above decimal point
in dividend.
Dividing by a Decimal Number
What do you do with the decimal point in division?
In division, a quotient (the result) is not changed when the dividend and divisor are both
multiplied by the same number. This is another use for the identity element.
Example:
Divide 7.2 (dividend) by 0.9
(divisor)
If we multiply both the
dividend and divisor by 10,
the new division allows us to
divide by whole numbers.
Note! Change the divisor (bottom) to a whole
number. Do this by multiplying both top and
bottom by 10 enough times to make the
divisor into a whole number.
Check: 8 × 0.9 = 7.2? Yes!
Example:
Divide a decimal by another decimal:
Divide 131.88 by 4.2
.
Remember the identity element? Choose an identify element to make the
denominator a whole number. For this example let’s use
 .
Multiply numerator by 10: 131.88 ×10 = 1318.8
Multiply denominator by 10: 4.2 × 10 = 42
Note! Move the decimal to the right enough to
make the divisor (bottom) a whole number.
Move the dividend’s (top) decimal the same
amount.
Note! Place decimal point in quotient directly
above new decimal location in dividend.
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