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.
Example
Name the following numbers:
1) \(203.65\) = Two hundred three and sixty-five hundredths
2) \(2.008\) = Two and eight thousandths
Example
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 bought 3 items: one for $4.50, one for $0.35 and one for $15.04. What was your total?
Solution
The total price is the sum of the prices of each individual item.
\[4.50+0.35+15.04=$18.98\]
Example 2
The price of a jacket originally costing $80.89 was discounted by $15.49. What is the new price of the jacket?
Solution
We have to subtract the discount from the original price.
\[Original \; price - discount = 80.89-15.49 = $65.40\]
Example 3
Using the formula \(Interest = Principal \times rate \times time\), what is the interest earned on a principal of $1000 with an interest rate of \(4%\) over 5 years?
Solution
We need to multiply $1000 by 0.04 and 5 to get the total interest.
\[1000 \times 0.04 \times 5 = $200\]
The interest earned is $200.
Example 4
You paid $128.94 for 6 lamps. How much does each lamp cost?
Round to the nearest cent.
Solution
\[6\overline{)128.94}=21.49\]
Each lamp costs $21.49.
