Expansion of Decimal Numbers
Expanded Form of Decimal Numbers
Here, we will discuss about the expanded form of decimal numbers. In expanded form of decimal numbers we see that, how to read and write the decimal numbers.
Expanded form means writing each digit in its given place value and add them all together.
Expanded form of any number with decimals is expressed using place value chart.
First we see the expansion of whole numbers (without decimal).
The place value refers to the value of a digit in a number starting from right to left. The value for each number is calculated by the position of the number.
Let us consider the number 5264. We expand each of the digits using place value chart.
we can rewrite the number as
5264 = 5000 + 200 + 60 + 4
Five thousands + two hundreds + six tens + four ones
5264 → 5 x 1000 + 2 x 100 + 6 x 10 + 4 x 1
Example: The number 345, write in expanded form.
The expanded form of 345 is 300 + 40 + 5
Three hundreds + four tens + five ones
Now we see the expansion of decimal numbers.
Let us consider the number 7.354
In words we would say that the number is seven and three hundred fifty four thousandths.
The whole number 7 is said as seven, the decimal is said as “and” and the decimal part which is 354, is said as regular number three hundred fifty four.
But it is a decimal , we would say the last number as its place value.
The last number four is in the thousandths place, so we must say three hundred fifty four thousandths.
Write in expanded form.
(1) 3.05
| Ones | Tenths | Hundredths |
| (1) | (1/10) | (1/100) |
| 3 | 0 | 5 |
3.05 = 3 x 1 + 0 x 1/10 +5/100
(2) 30.05
| Tens | Ones | Tenths | Hundredths |
| (10) | (1) | (1/10) | (1/100) |
| 3 | 0 | 0 | 5 |
30.05 = 3 x 10 + 0 x 1 + 0 x 1/10 +5 x 1/100
(3) 3.054
| Ones | Tenths | Hundredths | Thousandths |
| (1) | (1/10) | (1/100) | (1/1000) |
| 3 | 0 | 5 | 4 |
3.054 = 3 x 1 + 0 x 1/10+ 5 x 1/100 +4 x 1/1000
(4) 300.05
| Hundred | Tens | Ones | Tenths | Hundredths |
| (100) | (10) | (1) | (1/10) | (1/100) |
| 3 | 0 | 0 | 0 | 5 |
300.05 = 3 x 100 + 0 x 10+ 0 x 1 + 0 x 1/10 + 5 x 1/100
Write in expanded form.
(1) 2568.437
Solution: 2568.437 = 2 thousands + 5 hundreds + 6 tens + 8 ones + 4 tenths + 3 hundredths + 7 thousandths
= 2000 + 500 + 60 + 8 + 4/10 + 3/100 + 7/1000…..(Fractional expansion)
= 2000 + 500 + 60 + 8 + 0.4 + 0.03 + 0.007…..(Decimal expansion)
(2) 4576.324
Solution: 4576.324 = 4 thousands + 5 hundreds + 7 tens + 6 ones + 3 tenths + 2 hundredths + 4 thousandths
4000 + 500 + 70 + 4 + 3/10 + 2/100 + 4/1000…..(Fractional expansion)
= 4000 + 500 + 70 + 4 + 0.3 + 0.02 + 0.004…..(Decimal expansion)
(3) 385.4
Solution: 385.4 = 3 hundreds + 8 tens + 5 ones + 4 tenths
= 300 + 80 + 5 + 4/10
(4) 45.23
Solution: 45.23 = 4 tens + 5 ones + 2 tenths + 3 hundredths
45.23 = 40 + 5 + 2/10 + 3/100
= 40 + 5 + 0.2 + 0.03
(5) 635.51
Solution: 635.51 = 6 hundreds + 3 tens + 5 ones + 5 tenths + 1 hundredths
= 600 + 30 + 5 + 5/10 + 1/100
(6) 0.258
Solution: 0.258 = 0 ones + 2 tenths + 5 hundredths + 8 thousandths
= 0 + 2/10 + 5/100 + 8/1000
= 2/10 + 5/100 + 8/1000
(7) 5.5
Solution: 5.5 = 5 ones + 5 tenth
= 5 + 5/10
(8) 4.259
Solution: 4.259=4 ones + 2 tenths + 5 hundredths + 9 thousandths
4.259 = 4 + 2/10 + 5/100 + 8/1000
(9) 63.5028
Solution: 63.5028 = 6 tens + 3 ones + 5 tenths + 0 hundredths + 2 thousandths + 8 ten thousandths
= 60 + 30 + 5/10 + 0/100 + 2/1000 + 8/10000
(10) 5241.908
Solution: 5 thousands + 2 hundreds + 4 tens + 1 ones + 9 tenths + 0 hundredths + 8 thousandths
5000 + 200 + 40 + 1 + 9/10 + 0/100 + 8/1000
(11) 1234.56
Solution: 1 thousands + 2 hundreds + 3 tens + 4 ones + 5 tenths + 6 hundredths
1000 + 200 + 30 + 4 + 5/10 + 6/100
(12) 187.657
Solution: 1 hundreds + 8 tens + 7 ones + 6 tenths + 5 hundredths + 7 thousandths
100 + 80 + 7 + 6/10 + 5/100 + 7/1000
Example: Expansion of 35.248
10←35.248→1/1000
↗ ↑ ↖
1 1/10 1/100
3 x 10 + 5 x 1 + 2 x 1/10 + 4 x 1/100 + 8 x 1/1000
Example: Expansion of 76.589
10←76.589→1/1000
↗ ↑ ↖
1 1/10 1/100
7 x 10 + 6 x 1 + 5 x 1/10 + 8 x 1/100 + 9 x 1/1000