How To Multiply Numbers Ending In Zero
Actually, no matter what the number is, you can multiply any kind of number using the long multiplication method, but for numbers ending in zero, you can use the short multiplication method.
40 x 30
Ignore the Zeros at First
f you're multiplying two numbers that end in zero, such as 40 and 30, you can initially ignore the zeros and multiply the remaining numbers. In this case, 4 * 3 = 12.
Count the Zeros
Next, count the total number of zeros at the end of both numbers. In this example, there are two zeros (one from 40 and one from 30)
Add the Zeros Back:
Add the zeros back to the product by appending as many zeros as you counted in step 2. In this example, you would add two zeros to 12, resulting in 1200
Check Your Work:
You can always check your work using a calculator or another method of multiplication.
40 x 25
Ignore the Zero:
Ignore the zero at the end of 40 and multiply 4 by 25, which equals 100.
Count the Zeros:
Count the total number of zeros at the end of the number 40, which is one in this case.
Add the Zero Back:
Add one zero to 100, resulting in 1000.
So, 40 * 25 = 1000.
1200 x 30
Ignore the Zeros:
Ignore the zeros at the end of 1200 and 30, and multiply 12 by 3, which equals 36.
Count the Zeros:
Count the total number of zeros at the end of both numbers, which is four in this case (three from 1200 and one from 30).
Add the Zeros Back:
Add four zeros to 36, resulting in 36000.
So, 1200 * 30 = 36000.
Why is this method valid ?
Understanding Place Value:
In the decimal number system, each digit has a value that is 10 times smaller as you move to the right. For example, in the number 1200, the "1" is in the thousands place, the "2" is in the hundreds place, and the two zeros are in the tens and units places.
Zero's Multiplication Property:
When you multiply any number by zero, the result is zero. This means that when you multiply numbers ending in zero, many of the steps will be zero, simplifying and speeding up the process.
Zero's Place Value:
A zero at the end of a number signifies that the number is a multiple of 10, 100, 1000, etc. This means that when you multiply numbers ending in zero, you can temporarily ignore the zeros and then add them back to the result.
Example:
In the example of 1200 * 30:
You multiply 12 and 3 (ignoring the zeros), resulting in 36.
You count the total number of zeros at the end of both numbers (four in this case).
You add four zeros to the end of the result, making it 36000.
This shortcut leverages the special properties of zero in multiplication and the place value in the decimal system. Therefore, this method is mathematically valid and an efficient way to multiply numbers that end in zero.
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