Place Value: Decimals Comparisons and Hundredths Place in Decimals

There are terms that describe place value for decimals in the same way that those terms describe place value for whole numbers, such as tenths, hundredths, thousandths, ten thousandths, hundred thousandths, millionths, etc. Beginning with the first numeral after the decimal point, these terms are used from left to right.

In the number 0.1234, there is a “1” in the tenths place, a “2” in the hundredths place, a “3” in the thousandths place, and a “4” in the ten-thousandths place. The number 78.304 has a “7” in the tens place, an “8” in the one’s place, a “3” in the tenths place, a “0” in the hundredths place, and a “4” in the thousandths place.

As we use base ten, a value of 10 in one place is equal to a value of 1 in the place to the left: one-thousandth is equivalent to one hundredth, ten-hundredths is equivalent to ten tenths, and so on.

Example 1. What are the place values for 67.0534?

Sixteen is in the Tens place, seven is in the One’s place, ten is in the Tenths place, five is in the Hundredths place, three is in the Thousandths place, and four is in the Ten Thousandths.

Place Value: Decimals

A Fact about Decimals

Adding zeros at the end of a decimal does not cause the decimal to change. The number 3.45 is equivalent to 3.450 is equivalent to 3.4500, and so on.

Comparing Decimals

When two decimals are equal, it can be difficult to determine which is larger. The first glance suggests that 0.304 is greater than 0.62 because 304 is greater than 62. However, this is not the case. In order to determine which decimal is larger, we must compare the two place-by-place, starting from the tenths place, until the decimals differ. The tenths place of 0.304 is a “3”, and the tenths place of 0.62 is a “6”. Since 6 is greater than 3, then 0.62 is greater than 0.304. Further decimal places do not need to be taken into account.

Example 2. Compare 0.4531 and 0.4507. Which is greater?

There is a “4” in the tenth place in both 0.4531 and 0.4507.
For both 0.4531 and 0.4507, the hundredth place is marked with a “5”.
0.4507 has a “0” in the thousandths place and 0.4531 has a “3” in the thousandths place.
Since 3 is greater than 0, 0.4531 is greater than 0.4507.

Hundredths Place in Decimals

Whenever we write a decimal number with two places, we are representing the hundredth place. Let us take a plane sheet that represents one whole. Now, we divide the sheet into 100 equal parts. 

Each part represents one-hundredths of the whole. It is written as 11001100. In the decimal form, it is written as 0.01. In the hexadecimal form, it is written as 1.

Represents 3510035100 on a square sheet. 

35 parts of hundred equal parts are colored. In decimal form, this is 0.35, where 3 represents three tenths and 5 represents five hundredths. In the place value chart 3 is written in the tenths column and 5 is written in the hundredths column.

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