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: A patient receives the following doses of medication every day: 0.2 mg, 1.05 mg and 2.84 mg. What is the total daily dosage?
Solution
The total daily dosage is the sum of the individual dosages.
\[0.2+1.05+2.84=4.09\,mg\]
Example 2: A patient's temperature reading in the morning was \(102.3^{\circ}F\). In the afternoon, their temperature was \(98.5^{\circ}F\). What is the decrease in temperature?
Solution
We have to subtract the afternoon temperature from the morning temperature.
Temp decrease = morning - afternoon = 102.3 - 98.5 = 3.8.
The temperature decrease was \(3.8^{\circ}F\).
Example 3: A patient weighs 80.4 kg. One kg is 2.2 lbs. What is the patient's weight in pounds?
Solution
We need to multiply 80.4 kg by 2.2 lbs to find the weight in pounds.
\[80.4\times 2.2=176.88\,lbs\]
The patient weighs 176.88 lbs.
Example 4: A nurse is pouring servings of juice from a pitcher with 1050 mL of juice. How many 150 mL servings can she pour?
Solution
For long division, you need to divide the whole (1050 mL) by the part (150 mL).
\[150\overline{)1050}=7\]
The nurse can pour 7 servings of juice.
