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Lesson 3: Decimals in expanded form

# Decimals in expanded form review

Review writing decimals in expanded form, and try some practice problems.

## Expanded form

Expanded form is a way to write numbers by adding the value of its digits.
We can use a place value chart to think of the value of a number's digit.

### Example

Let's write $3.405$ in expanded form.
Ones.TenthsHundredthsThousandths
$3$.$4$$0$$5$
$\phantom{3.405}=\left(3×1\right)+\left(4×\frac{1}{10}\right)$$+\left(0×\frac{1}{100}\right)+\left(5×\frac{1}{1000}\right)$
$\phantom{3.405}=3+\frac{4}{10}+0+\frac{5}{1000}$
$3.405$ in expanded form is $3+\frac{4}{10}+\frac{5}{1000}$.

## Practice

Problem 1
$57.142=\phantom{\rule{0.167em}{0ex}}?$

Want to try more problems like this? Check out this exercise.

## Want to join the conversation?

• Why are decimals so hard? I mean I get all the practice and they just seem so hard once I do them.
• Sometimes the concepts give us fits and are hard to understand. You just need to keep practicing, and then before too long you'll have that "AHA" moment where it will all make sense.

Sometimes I recommend using money to work with decimals. After all, $3.95 and$79.50 are decimals, and if you practice adding money (two items at $3.95), how much will your bill be? If you practice subtracting money (something costs$9.37 and you give a \$10.00 bill, how much change will you get)

Keep at it. You can do it!!
• I don't understand the practice for Decimals in expanded form, Can someone help
• Basically in a decimal, there are 4 places,

ones. tenths | hundredths | thousandths

so for example here is a decimal, 4.209

4, is in the ones place
2, is in the tenths place
0, is in the hundredths place
9, is in the thousandths place.

So expanded form is just add the ones, tenths, hundredths, and thousandths place together

For example,

We have our decimal 4.209,

so the expanded form is 4 + 0.2 + 0.00 0.009
• Why did math became so popluar
• it did not just people had to use it a lot
• i don't understand (8x1000)+(6x100)+(2x10)+(4x1+(3x1/100)
• You do all the things in () first before adding them all together. Your question's answer is 8,624.03
• my "Decimals in expanded from" doesn't work so it put me here.😅
• Why we can have hundredths and tenths, but not oneths
• In the context of decimal place values, it's important to understand the concepts of "hundredths" and "tenths." A "hundredth" is equal to 1 divided by 100, which can be represented as 1/100. Similarly, a "tenth" is equal to 1 divided by 10, or 1/10.

Now, let's consider the term "oneth." Following the same logic, one might assume that "oneth" would be equal to 1 divided by 1, which is simply 1. Therefore, "oneths" are not logically meaningful in the context of fractions.

In reality, when we divide 1 into 10 equal parts, we call each of these parts a "tenth." Likewise, if we were to divide 1 into 100 equal parts, each part would be referred to as a "hundredth," and so on.

I hope this clarifies the relationship between decimal place values and fractions for you.
• what would 345.609 be in expanded from
• 300+40+5+.6+.009
• what digit is after thousandths?