Understanding Place Value

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Topic Content:

Meaning of Place Value
Rules for Finding Place Value
Worked Examples
Place Value Rush
Final Evaluation

What is Place Value?

Place value is the value of a digit in a number based on its place or position.

Each digit, whole number or decimal number has a place value based on its position.

The value of a digit in the number is the digit multiplied by the place value.

Example: 9783 . 2465

Place Value:	Expanded Form:	Value:
9 is in thousands	9 × 1000	9000
7 is in hundreds	7 × 100	700
8 is in tens	8 × 10	80
3 is in units/ones	3 × 1	3
2 is in tenths	2 × \( \frac{1}{10}\)	0.2
4 is in hundredths	4 × \( \frac{1}{100}\)	0.04
6 is in thousandths	6 × \( \frac{1}{1000}\)	0.006
5 is in ten thousandths	5 × \( \frac{1}{10000}\)	0.0005
		Sum = 9783.2465

Rules for Finding Place Value:

Below are the place value rules for the number 9783.2465 above;

Whole Numbers:

For whole numbers, always start from the decimal point and move to the left.
The first digit to the left of the decimal point is in the units/ones place, i.e. 3 units.
The second digit to the left of the decimal point is in the tens place, i.e. 8 tens.
The third digit to the left of the decimal point is in the hundreds place, i.e. 7 hundreds.
The fourth digit to the left of the decimal point is in the thousands place, i.e. 9 thousands.

Decimal Numbers:

There is no decimal place value called “units” after the decimal point. Decimal place values start from tenths.
The first digit to the right of the decimal point is in the tenths place, i.e. 2 tenths.
The second digit to the right of the decimal point is in the hundredths place, i.e. 4 hundredths.
The third digit to the right of the decimal point is in the thousandths place, i.e. 6 thousandths.
The fourth digit to the right of the decimal point is in the ten-thousandths place, i.e. 5 ten-thousandths.

Now let’s try some more examples.

Worked Example 1.1.1:

Give the digits in ones place and tenths place in the number 75.39

Solution:

Step 1:

75.39

In the given number 75.39, the digit in ones place is 5 as it is the first digit to the left of the decimal point.

Step 2:

75.39

The digit in tenths place is 3 as it is the first digit to the right of the decimal point.

Worked Example 1.1.2:

Write down the place values for all the numbers in 9 453 276 . 1847

Solution:

9 – Millions
4 – Hundred thousands
5 – Ten thousands
3 – Thousands
2 – Hundreds
7 – Tens
6 – Units

. = Decimal point

1 – Tenths
8 – Hundredths
4 – Thousandths
7 – Ten thousandths