EXPANDED FORM OF DECIMAL NUMBER -
To expand a decimal number, you express each digit in its appropriate place value position. Let's use the decimal number 25.376 as an example:
2 x 10 + 5 x 1 + 3 x 0.1 + 7 x 0.01 + 6 x 0.001
Expanding each digit according to its place value, we get:
(2 x 10) + (5 x 1) + (3 x 0.1) + (7 x 0.01) + (6 x 0.001)
Simplifying the calculations:
20 + 5 + 0.3 + 0.07 + 0.006
Adding these values together:
25 + 0.3 + 0.07 + 0.006
The expanded form of the decimal number 25.376 is:
25 + 0.3 + 0.07 + 0.006 = 25.376 (Ans.)
To expand a decimal number, you can express it as the sum of its place values. Here's an example using the decimal number 25.376:
25.376 = (2 × 10) + (5 × 1) + (3 × 0.1) + (7 × 0.01) + (6 × 0.001)
Expanding the decimal number in this way breaks it down into its constituent place values. Each digit is multiplied by the corresponding power of 10 based on its position from left to right. In this case:
2 is in the tens place, so it is multiplied by 10.
5 is in the ones place, so it is multiplied by 1.
3 is in the tenths place, so it is multiplied by 0.1 (10^-1).
7 is in the hundredths place, so it is multiplied by 0.01 (10^-2).
6 is in the thousandths place, so it is multiplied by 0.001 (10^-3).
Adding up all these products gives us the expanded form of the decimal number. In this case, the expanded form of 25.376 is:
25.376 = 20 + 5 + 0.3 + 0.07 + 0.006. (Ans.)
We know the place value of each digit in 468.356
So, we can write 468.356 in the expanded form as indicated below: -
468.356 = 4 hundreds + 6 tens + 8 ones + 3 tenths + 5 hundredths + 6 thousandths
3 5 6
= 400 + 60 + 8 + ------+ ------ + -------
10 100 1000
= 400 + 60 + 8 + 0.3 + 0.05 + 0.006 (Ans.)
4 8
a) 0.48 = 0 + ------ + ------ = 0 + 0.4 + 0.08 (Ans.)
10 100
7 1 4
b) 0.714 = 0 + ------- + ------- + --------
10 100 1000
= 0 + 0.7 + 0.01 + 0.004 (Ans.)
1 5
g) 5.015 = 5 + ------- + -------
100 1000
= 5 + 0.01 + 0.005 (Ans.)
4 2 6
h) 815.426 = 800 + 10 + 5 + ------- + ------- + -------
10 100 1000
= 800 + 10 + 5 + 0.4 + 0.02 + 0.006 (Ans.)