Introduction to Decimals Study Guide (page 2)

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Updated on Oct 4, 2011

Adding Zeroes

Adding zeroes to the end of the decimal does NOT change its value. For example, 6.017 has the same value as each of these decimals:





6.01700000, and so forth

Remembering that a whole number is assumed to have a decimal point at its right, the whole number 6 has the same value as each of these:




6.000, and so forth

On the other hand, adding zeroes before the first decimal digit does change its value. That is, 617 is NOT the same as 6.017.


Decimals are all around us! They are used in money, measurement, and time, so it's important to read this section carefully and make sure you feel comfortable with them. Using decimals is essential in mastering practical, real-world math skills.

Changing Decimals to Fractions and Fractions to Decimals

Changing Decimals to Fractions

To change a decimal to a fraction:

  1. Write the digits of the decimal as the top number of a fraction.
  2. Write the decimal's name as the bottom number of the fraction.

Example: Change 0.018 to a fraction.

1. Write 18 as the top of the fraction: 18
2. Since there are three places to the right of the decimal, it's thousandths.
3. Write 1,000 as the bottom number:
4. Reduce by dividing 2 into the top and bottom numbers:

Changing Fractions to Decimals

To change a fraction to a decimal:

  1. Set up a long division problem to divide the bottom number (the divisor) into the top number(the dividend)—but don't divide yet!
  2. Put a decimal point and a few zeros on the right of the divisor.
  3. Bring the decimal point straight up into the area for the answer (the quotient).
  4. Divide.

Example: Change to a decimal.

1. Set up the division problem:
2. Add a decimal point and 2 zeroes to the divisor (3):
3. Bring the decimal point up into the answer:
4. Divide:

Thus, = 0.75, or 75 hundredths

Repeating Decimals

Some fractions may require you to add more than two or three decimal zeros in order for the division to come out evenly. In fact, when you change a fraction like to a decimal, you'll keep adding decimal zeros until you're blue in the face because the division will never come out evenly! As you divide 3 into 2, you'll keep getting 6s:

A fraction like becomes a repeating decimal. Its decimal value can be written as or , or it can be approximated as 0.66, 0.666, 0.6666, and so forth. Its value can also be approximated by rounding it to 0.67 or 0.667 or 0.6667, and so forth. (Rounding is covered later in this lesson.)

If you really have fractionphobia and panic when you have to do fraction arithmetic, just convert each fraction to a decimal and do the arithmetic in decimals. Warning: This should be a means of last resort—fractions are so much a part of daily living that it's important to be able to work with them.

Comparing Decimals

Decimals are easy to compare when they have the same number of digits after the decimal point. Tack zeros onto the end of the shorter decimals—this doesn't change their value—and compare the numbers as if the decimal points weren't there.

Example: Compare 0.08 and 0.1. (Don't be tempted into thinking 0.08 is larger than 0.1 just because the whole number 8 is larger than the whole number 1!)

  1. Since 0.08 has two decimal digits, tack one zero onto the end of 0.1, making it 0.10
  2. To compare 0.10 to 0.08, just compare 10 to 8. Ten is larger than 8, so 0.1 is larger than 0.08
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