Homework Help: Writing Decimals

How to Write Decimals

Like fractions, decimals can express amounts that are less than one. Just as you can use the fraction 1/2 to indicate that you ate half of a pie, you can use the decimal 0.5 to express the same idea.

The first three places to the right of the decimal point are the tenths, hundredths and thousandths places. For instance, in the decimal 1.234, the two is in the tenths place, the three is in the hundredths place and the four is in the thousandths place.

Number Names

Sometimes, you'll be given a decimal that's written out in words, like three-tenths, and you'll have to write it as a number. To do this, write the number (three) in the decimal place indicated (tenths), and then fill in any unoccupied decimal places to the left of the number with zeros. For example, three tenths would be written like this: 0.3. Here are a few more examples:

Two-tenths = 0.2

Four-hundredths = 0.04

Seven-thousandths = 0.007

Next, you'll learn to write decimals with multiple non-zero digits, like seventy-three thousandths. For decimals like these, write the number (seventy-three) so that its last digit (three) is in the place that's indicated (thousandths), like this: 0.073. Here are some other examples:

Two hundred and sixty-one thousandths = 0.261

Twenty-two hundredths = 0.22

Twenty-two thousandths = 0.022

Fractions

You may also be asked to write fractions as decimals. Since each place in a decimal represents a fraction of a base-ten number, like ten, 100 or 1,000, you'll be working with fractions that have these denominators. For fractions of ten, the numerator goes in the decimal's tenths place (6/10 = 0.6). For fractions of 100, the numerator goes in the hundredths place (6/100 = 0.06), and the numerator goes in the thousandths place for fractions of 1,000 (6/1,000 = 0.006).

When you're converting a fraction whose numerator has multiple digits, like 35/1,000, position the numerator so that its last digit (five) goes in the place that the fraction indicates (thousandths), like this: 0.035. These are additional examples:

234/1,000 = 0.234

23/1,000 = 0.023

23/100 = 0.23

Expanded Form

You'll also be asked to convert numbers that are in expanded form into decimals. A number is in 'expanded form' when it's expressed as the product of a whole number and a fraction of a base-ten number. For instance, 9/100 in expanded form is 9 x (1/100), since (9/1) x (1/100) = 9/100. Likewise, 25/1,000 is 25 x (1/1,000), because (25/1) x (1/1,000) = 25/1,000.

To write a number that's in expanded form as a decimal, convert it to a fraction first. Then, write it in decimal form using the method explained in the previous section about fractions. Here are a few examples:

8 x (1/10) = (8/1) x (1/10) = 8/10 = 0.8

27 x (1/100) = (27/1) x (1/100) = 27/100 = 0.27

789 x (1/1,000) = (789/1) x (1/1,000) = 789/1,000 = 0.789

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