The general form of a number
Letters for digits: …dcba = … + 1000d + 100c + 10b + a.
Digits as letter-numbers
When we do not know the digits of a number, we can use letter-numbers: a for the units digit, b for the tens, c for the hundreds and d for the thousands. The number is written dcba.
A number has d = 4, c = 0, b = 7, a = 5. What is dcba?
What this lesson covers
The idea
Any number can be written in general as …dcba = … + 1000d + 100c + 10b + a, where the letter-numbers a, b, c, d are its units, tens, hundreds and thousands digits.
Digits as letter-numbers
When we do not know the digits of a number, we can use letter-numbers: a for the units digit, b for the tens, c for the hundreds and d for the thousands. The number is written dcba.
A number has d = 4, c = 0, b = 7, a = 5. What is dcba?
- 4075
- 16
- 0
Build numbers from digits
Use ▲ ▼ to change each digit. Watch the expanded form fill in. The number is the sum of place values, each one multiplied by its digit.
Place value times digit
Any number can be written in general as …dcba = … + 1000d + 100c + 10b + a, where the letter-numbers a, b, c, d are its units, tens, hundreds and thousands digits.
In 4075: d = 4, c = 0, b = 7, a = 5. So 4075 = 1000 × 4 + 100 × 0 + 10 × 7 + 5.
dcba means the digits side by side. It is not d × c × b × a (that would be 0 here).
Notes
Any number can be written in general as …dcba = … + 1000d + 100c + 10b + a, where the letter-numbers a, b, c, d are its units, tens, hundreds and thousands digits.
Check yourself
In the number 6283, written dcba, what is the value of 10b?
Answer: 80
The tens digit of 6283 is 8, so b = 8 and 10b = 80.
A number dcba has d = 2, c = 5, b = 0, a = 3. What number is it?
Answer: 2503
1000 × 2 + 100 × 5 + 10 × 0 + 3 = 2000 + 500 + 0 + 3 = 2503.
A 5-digit number is edcba. Which expression gives its value?
In a number dcba the digit c is increased by 1. By how much does the number increase?
Answer: 100
The number contains 100c. When c becomes c + 1, the term becomes 100(c + 1) = 100c + 100. So the number increases by 100.
- e + d + c + b + a. That adds the digits. Each digit must be multiplied by its place value.
- 10000e + 1000d + 100c + 10b + a — correct. Yes! e is in the ten-thousands place, d in the thousands, and so on down to a in the units.
- 1000e + 100d + 10c + b + a. That shifts every place one step to the right. e is in the ten-thousands place.
- e × d × c × b × a. That multiplies the digits. edcba means the digits written side by side.