The dot represents a decimal point where place values are separated by what is to the left and right. To the right of the decimal points such as a tenth \(\frac{1}{10}\), a hundredth \(\frac{1}{100}\), and so on.
Examples
Name the following numbers:
1) \(203.65\) = Two hundred three and sixty-five hundredths
2) \(2.008\) = Two and eight thousandths
Examples
Write out the following numbers:
1) One thousand twenty-two and three tenths = \(1022.3\)
2) Eighty thousand and eighty thousandths = \(80,000.080\)
The decimal place value determines how to convert a decimal into a fraction.
Example \[0.045\]
ends at the thousandths place value. Therefore you put the number over 1000
\[=\frac{45}{1000}\]
Simplify the fraction
\[=\frac{9}{20}\]
See video below for more examples, including mixed fractions and converting from fractions back to decimals.
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Rounding Decimal Notation To round to a certain place:
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Example 1
Round \(0.084\) to the nearest tenth.
Solution
Locate the digit in the tenths place
\[0.\underline{0}84\]
Consider the next digit to the right, 8
Since 8 is greater than or equal to 5, round up.
\[0.1\]
Example 2
Round \(212.5604\) to the nearest hundredths
Solution
Locate the digit in the hundredths place
\[212.5\underline{6}04\]
Consider the next digit to the right, 0
Since 0 is 4 or lower, keep digit the same.
\[212.56\]
Example 1
You order 3 appetizers: one for $7.99, one for $12.49 and another for $15.89. How much did the appetizers cost?
Solution
The total is the sum of the individual appetizers.
\[7.99+12.49+15.89 = 36.37\]
The total for the appetizers was $36.37.
Example 2
A meal plus tip costs $75.83. If the meal alone costs $64.26, how much was the tip?
Solution
We have to subtract the meal price from the total price.
Total - Meal = \[75.83 - 64.26 = $11.57\]
The tip is $11.57.
Example 3
If one beverage costs $12.89 per bottle, how much will 15 bottles cost?
Solution
We need to multiply $12.89 by 15 to find the total cost.
\[12.89\times 15=$193.35\]
15 bottles cost $193.35.
Example 4
500 g of potatoes costs $3.50. How much do potatoes cost per gram?
Solution
\[500\overline{)3.50}=0.0068\]
Potatoes cost $0.0068/g
