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
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.
For 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.
\[0.1\]
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: Find the total resistance for the circuit diagram below. The total resistance of a series circuit is equal to the sum of the individual resistances.
Solution
The total resistance is the sum of the individual resistances in this series circuit.
\[2.34+37.5+.09=39.93\,ohms\]
Example 2: A series circuit containing two resistors has a total resistance (\(R_T\)) of 37.272 ohms. One of the resistors (\(R_1\)) has a value of 14.88 ohms. What is the value of the other resistor (\(R_2\))?
Solution
We have to subtract \(R_1\) from the total resistance \(R_T\).
\[R_2=R_T-R_1=37.272-14.88=22.392\,ohms\]
Example 3: Using the formula Watts = Amperes \(\times\) Voltage, what is the wattage of an electric drill that uses 9.45 amperes from a 120 volt source?
Solution
We need to multiply 120 amperes by 9.45 volts to find the wattage of the electric drill.
\[120\times 9.45=1134\,watts\]
The electric drill is 1134 watts.
Example 4: The wing area of an airplane is 262. square feet and its span is 40.4 feet. Find the mean chord of its wing using the formula: Area \(\div\) span = mean chord.
Solution
For long division, you want to work with a divisor that does not have a decimal value. We can transform it by multiplying both the dividend and divisor by 10.
\[40.4\overline{)262}=404\overline{)2620}=6.5\]
The mean chord is 6.5 feet.
