### Place Value for Decimals

Just like whole numbers have “ones,” “tens,” and “hundreds” to describe place value, decimals have terms like tenths, hundredths, thousandths, etc. These terms are used from left to right, starting with the first numeral after the decimal point. For example, in the number 0.1234, the “1” is in the tenths place, the “2” is in the hundredths place, the “3” is in the thousandths place, and the “4” is in the ten thousandths place. Similarly, in the number 78.304, the “3” is in the tenths place, the “0” is in the hundredths place, and the “4” is in the thousandths place.

### Key Facts

- Place Value for Decimals:
- Just like whole numbers have “ones,” “tens,” and “hundreds” to describe place value, decimals have terms like tenths, hundredths, thousandths, etc..
- These terms are used from left to right, starting with the first numeral after the decimal point.
- For example, in the number 0.1234, the “1” is in the tenths place, the “2” is in the hundredths place, the “3” is in the thousandths place, and the “4” is in the ten thousandths place.
- Similarly, in the number 78.304, the “3” is in the tenths place, the “0” is in the hundredths place, and the “4” is in the thousandths place.

- Relationship between Place Values:
- In our base ten system, a value of 10 in one place is equal to a value of 1 in the place to the left.
- For example, 10 thousandths is equivalent to 1 hundredth, 10 hundredths is equivalent to 1 tenth, and 10 tenths is equivalent to 1 one.

- Comparing Decimals:
- When comparing decimals, it is important to compare them place-by-place, starting from the tenths place.
- For example, to compare 0.304 and 0.62, we compare the digits in the tenths place. Since 6 is greater than 3, 0.62 is greater than 0.304.

### Relationship between Place Values

In our base ten system, a value of 10 in one place is equal to a value of 1 in the place to the left. For example, 10 thousandths is equivalent to 1 hundredth, 10 hundredths is equivalent to 1 tenth, and 10 tenths is equivalent to 1 one.

### Comparing Decimals

When comparing decimals, it is important to compare them place-by-place, starting from the tenths place. For example, to compare 0.304 and 0.62, we compare the digits in the tenths place. Since 6 is greater than 3, 0.62 is greater than 0.304.

### Conclusion

Decimals are a way of representing numbers that are not whole numbers. They are used in a variety of applications, such as measurement, finance, and science. Understanding the place value of decimals is essential for performing operations with decimals and for comparing decimals.

## Sources

- Place value with decimals (video) | Khan Academy (https://www.khanacademy.org/math/cc-fifth-grade-math/imp-place-value-and-decimals/imp-decimal-place-value-intro/v/place-value-with-decimals)
- Decimals: Place Value and Comparing Decimals | SparkNotes (https://www.sparknotes.com/math/prealgebra/decimals/section1/)
- Decimals – Tenths, Hundredths and Thousandths – Home Campus (https://my.homecampus.com.sg/Learn/Primary-Grade-4/Decimal/Understanding-Tenths-Hundredths-Thousandths)

## FAQs

### What are tenths, hundredths, and thousandths?

Tenths, hundredths, and thousandths are terms used to describe the place value of digits in a decimal number. Tenths are the digits to the right of the decimal point, hundredths are the digits two places to the right of the decimal point, and thousandths are the digits three places to the right of the decimal point.

### How do you read a decimal number?

To read a decimal number, start by reading the whole number part of the number. Then, read the decimal point as “point.” Finally, read the digits to the right of the decimal point as tenths, hundredths, thousandths, and so on.

### How do you compare decimals?

To compare decimals, start by comparing the digits in the tenths place. If the digits in the tenths place are different, then the decimal with the greater digit in the tenths place is greater. If the digits in the tenths place are the same, then compare the digits in the hundredths place. Continue comparing digits place-by-place until you find a difference. The decimal with the greater digit in that place is greater.

### How do you add and subtract decimals?

To add or subtract decimals, line up the decimal points of the two numbers. Then, add or subtract the digits in each place value column, starting with the tenths place. If there is a decimal point in the answer, make sure to line it up with the decimal points in the original numbers.

### How do you multiply decimals?

To multiply decimals, multiply the two numbers as if they were whole numbers. Then, count the total number of decimal places in the two original numbers and place the decimal point in the answer so that there are that many decimal places.

### How do you divide decimals?

To divide decimals, first convert the divisor (the number you are dividing by) to a whole number by moving the decimal point all the way to the right. Then, multiply the dividend (the number you are dividing) by the same power of 10 that you moved the decimal point in the divisor. Finally, divide the dividend by the divisor as if they were whole numbers. Place the decimal point in the answer directly above the decimal point in the dividend.

### What are some examples of decimals?

Some examples of decimals are 0.5, 1.25, 3.14, and 9.876.

### How are decimals used in real life?

Decimals are used in a variety of real-life applications, such as measurement, finance, and science. For example, decimals are used to measure the length of objects, the amount of money in a bank account, and the temperature of the air.