Decimals Place Value

So, what is place value of decimal?

Just like in a whole number value of digit in decimal depends on its place (position) in the number (before or after the decimal point).

The rightmost digit to the left of decimal point is ones, next to the left tens, next hundreds, then thousands, ten thousands, hundred thousands, millions, ten millions; etc.

The leftmost digit to the right of decimal point is tenths, next to the right hundredths, next thousandths, then ten thousandths, hundred thousandths, millionths, ten millionths; etc.

Example 1. Determine place value of each digit in 3156.24.

`\underbrace 3_(text(thousands))\quad\underbrace 1_(text(hundreds))\quad\underbrace 5_(text(tens))\quad\underbrace 6_(text(ones)).\underbrace 2_(text(tenths))\quad\underbrace 4_(text(hundredths))`

Next example involves more digits.

Example 2. Determine place value of each digit in 58,365.73874.

`\underbrace 5_(text(ten thousands))\quad\underbrace 8_(text(thousands))\quad\underbrace 3_(text(hundreds))\quad\underbrace 6_(text(tens))\quad\underbrace 5_(text(ones)).\underbrace 7_(text(tenths))\quad\underbrace 3_(text(hundredths))\quad\underbrace 8_(text(thousandths))\quad\underbrace 7_(text(ten thousandths))\quad\underbrace 4_(text(hundred thousands))`

Also note, that every integer can be written as decimal. Just add zeros after decimal point.

So, integer 487 is equivalent to 487.0 or 487.00 etc.

In general, we can ignore trailing zeros after decimal point.

For example, 375.28000 is same as 375.28.

Warning! Only trailing zeros can be ignored. For example 15.04 IS NOT the same as 15.4.

But 15.04000 is same as 15.04.

Now, it is your turn. Take a pen and paper and solve following problems:

Exercise 1. Determine place value of each digit in 56.893.

`\underbrace 5_(text(tens))\quad\underbrace 6_(text(ones)).\underbrace 8_(text(tenths))\quad\underbrace 9_(text(hundredths))\quad\underbrace 3_(text(thousandths))`

Now, slightly harder exercise.

Exercise 2. Determine place value of each digit in 2758.7814.

`\underbrace 2_(text(thousands))\quad\underbrace 7_(text(hundreds))\quad\underbrace 5_(text(tens))\quad\underbrace 8_(text(ones)).\underbrace 7_(text(tenths))\quad\underbrace 8_(text(hundredths))\quad\underbrace 1_(text(thousandths))\quad\underbrace 4_(text(ten thousandths))`