In this lesson, we will learn the value of decimal places to the thousandths and how to write them in expanded form using decimals as well as fractions.
What is a decimal?
A decimal is a number that means part of a whole.
The digits, or number, in front of a decimal, represents a whole number. The digits, or number, after a decimal, represents a fraction.
Basically, the decimal separates the whole part and the fraction part of a number.
For example, if you have one apple, we would write that as 1.0
If someone ate half of the apple, then we no longer have one whole apple or 1 apple, but we have half of the apple. And, we can write that in decimal form as 0.5
Here is a table showing all the decimal places to the thousandths.
| 0.1 | 0.01 | 0.001 |
| \(\frac{1}{10}\) | \(\frac{1}{100}\) | \(\frac{1}{1000}\) |
| One-tenth | One-hundredth | One-thousandth |
Expanded form in decimals
Writing decimals in expanded form means writing each number according to its place value. This is done by multiplying each digit by its place value and adding them together. Let's take 7.426.
For example, 7.426 in the expanded form is written as below:
The whole number 7 has a place value of one, so we multiply by 7 by 1 and put parentheses around it to separate it from the other numbers: ( \(7\times 1\))
Next, we have the digit 4 in the tenths place so we multiply that by 0.1: ( \(4\times 0.1\))
Next, we have the digit 2 in the hundredths place, we multiply that by 0.01: (\(2\times 0.01\))
Finally, we have the digit 6 in the thousandths place, we multiply that by 0.001: (\(6\times 0.0001\))
The last step is finding the sum: ( \(7\times 1\)) + ( \(4\times 0.1\)) + (\(2\times 0.01\)) + (\(6\times 0.0001\))
Seven and four-tenths two-hundredths six-thousandths
Or, Seven and four hundred twenty-six thousandths.
Expanded form as fractions
We can also write decimals in expanded form using their fraction form. Let's once again look at the decimal place value table given above.
Taking the same example of 7.426, we write it in expanded form as fractions.
The whole number will stay the same as (\(7\times 1\))
Next, we'll have the digit 4 written as (4 × \(\frac{1}{10}\))
Next, we'll have the digit 2 written as ( 2 × \(\frac{1}{100}\))
Next, we'll have the digit 6 written as (6 × \(\frac{1}{1000}\))
Finally, we add them together just as we did before:
(\(7\times 1\)) + (4 × \(\frac{1}{10}\)) + ( 2 × \(\frac{1}{100}\)) + (6 × \(\frac{1}{1000}\))
In summary, when writing decimals in expanded form, we must always remember the following steps:
Step 1. Multiply all numbers by their place value
Step 2. Separate them using parentheses
Step 3. Add all numbers together to show them as a sum.
Remember
