Decimals Study Guide: GED Math (page 2)
Practice problems for these concepts can be found at:
Writing and Recognizing Decimals
If you've ever gone shopping, then you are familiar with decimals, because decimals are often used to represent amounts of money. Like fractions, decimals represent parts of whole numbers. For example, you know that $1.50 is neither one whole dollar nor two whole dollars. It's one dollar and one-half of another dollar, or 1.5 dollars. Another way to write 1.5 is .
How to Read a Decimal
Notice that decimals are numbers written with a dot or period either to the far left or somewhere in the middle. The dot is called a decimal point. The numbers to the left of the decimal point are whole numbers. Those to the right of the decimal point are fractions, or parts, of whole numbers.
You already know that each digit in the number 1,234 represents a place value, or a position in the number. So, for example, the 1 in 1,234 stands for one thousand. The 2 stands for two hundreds. The 3 stands for three tens. And the 4 stands for four ones. These are the place values that occur to the left of a decimal point. Each digit to the right of a decimal point also has a place value.
When you see a decimal, here's how to read it.
Step 1 Begin reading from left to right. Read the part of the number that is to the left of the decimal point as you would any other whole number.
Step 2 Read the decimal point as the word and.
Step 3 Read the number to the right of the decimal point as you would any other number. But then follow it with the name of the decimal place. You can determine the name of the decimal place by counting the number of digits to the right of the decimal point.
Write out the following decimal in words: 12.304
Begin reading from left to right. Read the part of the number that is to the left of the decimal point as you would any other whole number. The number to the left of the decimal point is 12. So you would write (or say if you were reading aloud) "twelve."
Read the decimal point as the word and. So you would next write "and."
Read the numbers to the right of the decimal point as you would any other similar group of numbers. But then follow with the name of the last decimal place. There are three numbers to the right of the decimal point, so the last place value is called thousandths. You would write "three hundred four thousandths."
So, the decimal 12.304 can be written in the following words: "twelve and three hundred four thousandths."
Decimal numbers are easy to compare and order, when you remember that the place value has meaning. However, trailing zeros to the right of the decimal point are disregarded. In math, 2.4 is the same number as 2.400 because both numbers represent 2 and 4 tenths. A whole number is understood to have a decimal point to the right of the number. For example, 21 = 21. = 21.0 = 21.000. Each expression represents 21 with no remainder.
Notice that the decimal in the example has a zero in the middle: 12.304. This zero happens to be in the hundredths place. It tells you that there are no hundredths in the number. However, there are tenths and thousandths, so the zero serves as a placeholder between the 3 and the 4. When a zero falls in between two numbers, it serves as a placeholder, and it affects the value of the number.
To compare decimals, it is best to change each decimal into an equivalent decimal with the same number of decimal places. Try ordering the numbers from least to greatest: .016, 0.7, .203, .75. Because some of the numbers have three places to the right of the decimal point, change each decimal to an equivalent decimal with three decimal places to the right of the decimal point. One of the numbers shows a leading zero; also include this leading zero in all of the numbers:
- 0.016, 0.700, 0.203, 0.750
Now the decimals can be compared in the same manner as whole numbers, and 16 < 203 < 700 < 750, so the answer is .016, .203, 0.7, .75.
Converting between Fractions and Decimals
To convert a fraction to a decimal, recall that means 1 divided by 4. Divide 1 by 4 to get the decimal equivalent of 0.25. To convert a decimal to a fraction, use the place value names for decimals. Rewrite the decimal as the named fraction, and then simplify the fraction. For example, 0.018 is read as "eighteen thousandths," which is Now simplify:
Common Fraction and Decimal Equivalents
Although you can always convert a fraction to a decimal by dividing the numerator by the denominator, it's a good idea to know common decimal and fraction equivalents for the GED. Here are some common decimals and fractions you might want to learn.
Decimal and Fraction Equivalents to Know
Practice problems for these concepts can be found at:
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