You're probably glad to know how to solve the problem, but you may be wondering why this process works. Well, don't worry! We're going to explain it using exponents.
To understand this process, we need to be familiar with a couple of facts. The first is writing 100 and 1000 as powers of 10. Observe the following:
100 = 10 x 10 = 10 2
1000 = 10 x 10 x 10 = 10 3
We know that 100 = 10 2 and that 1000 = 10 3. Notice that the exponents are equal to the number of zeros in the number. Basically, to write these numbers as powers of 10, count the number of zeros in the number, then raise 10 to that power. This corresponds to the first and second steps of the solving process, and we find the following:
100 x 1000 = 10 2 x 10 3
The next fact that we need to be familiar with is the multiplication rule of exponents. This rule states that
Multiplication Rule of Exponents  |
We know that a b x a c = a b+c. We can apply this to multiplying 10 2 x 10 3. This corresponds to the third step of the solving process, and we find the following:
100 x 1000 = 10 2 x 10 3 = 10 2+3 = 10 5
The last step in the solving process is calculating 10 5, which is 100000. Altogether, we find that:
100 x 1000 = 10 2 x 10 3 = 10 2+3 = 10 5 = 100000
Pretty neat, huh? We basically just walked through an informal proof that 100 x 1000 = 100000. What's even better is that this process of solving can be extended to any multiplication problem that multiplies powers of 10 together.
For example, suppose you enter a contest to win ten thousand $100 bills. You want to know how much money that actually is, so you need to multiply 100 x 10000. These are both powers of 10, so you can take it through the steps outlined in the first section of this lesson to solve.
First, count the number of zeros in 100, which is 2. Then, count the number of zeros in 10000, which is 4. Add up those zeros to get 2 + 4 = 6. Finally, write the number 1 and follow it with 6 zeros to get 1000000. We see that 100 x 10000 = 1000000. Breaking this down into powers of ten and using the exponent rule shows us the following:
100 x 10000 = 10 2 x 10 4 = 10 2+4 = 10 6 = 1000000
We see we get the same answer, which was to be expected. This tells you that if you win the contest, you get $1,000,000! Wow! Here's hoping!
Multiplying 100 x 1000 is really pretty easy when we break it down into steps, as is any multiplication problem involving powers of 10. This is a great process to put to memory for future reference!
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FAQs
Solution. When we multiply 100 by 1000, we get 100,000.
How to multiply by 10, 100, and 1000? ›
To multiply by 10, move the digits to the left by one place. To multiply by 100 move the digits to the left by two places. Don't forget to put a zero in the units if needed. To multiply by 1000 move the digits to the left by three places.
How to multiply big numbers easily? ›
How do you multiply large numbers? To multiply large numbers, start by multiplying the ones place of one number by the other number. Follow by multiplying the tens, then thousands, and so on, by the other number but place a zero as a placeholder to move the product to the correct place value.
Why is 100% 10% 1000? ›
A simple way to understand this is to look at what dividing by 10% means. We know that 10% is the same as 1/10. Dividing by 1/10 is the same as multiplying by 10. So 100%/10% is the same as 100% * 10, which is clearly 1000%.
How many times 3 occurs from 100 to 1000? ›
Answer: 3 occurs 90 times in tens and 90 times in the unit place in the numbers from 100 to 1000.
What are the multiples of 100 up to 1000? ›
The first 10 multiples of 100 are: 100, 200, 300, 400, 500, 600, 700, 800, 900 and 1000.
What is the rule for multiplying by 1000? ›
To multiply by 1000, you move the digits three place value places to the left. So 0.04 × 1000 = 40.
What is the fastest trick to multiply? ›
One of the best and easy multiplication tricks for large numbers is to find the tens of one of the numbers, and multiply with that quickly. Adding the remaining leftovers will be easier to calculate fully. E.g., 22 X 83 can be rewritten as (20 X 83) + (2 X 83) which gives us 1660 + 166 = 1826.
What is the hardest number to multiply? ›
The hardest multiplication is 6×8, which students got wrong 63% of the time. This was closely followed by 8×6, then 11×12, 12×8 and 8×12. The easiest multiplication, on the other hand, was 1×12, which students got wrong less than 5% of the time, followed by 1×6 and 9×1.
What is the mental math strategy for multiplication? ›
Front-end multiplication
This strategy involves expanding the larger factor into its place values and multiplying each place value separately to the smaller factor. Then, add all the products together. As an example, 4 x 352 is the same as 4 x 300 (1200) and 4 x 50 (200) and 4 x 2 (8).
Multiply or divide by 10, 100 or 1000
Place 0 in the space as a placeholder. Multiplying by 100: Move all the digits 2 places to the left. Place 0 in the spaces as placeholders. Multiplying by 1000: Move all the digits 3 places to the left.
How many 100 are in 1000? ›
There are 10 100s in 1,000.
What are 10 100 and 1000 called? ›
Numbers starting with a 1 and followed by only 0s (such 10, 100, 1,000, 10,000, and so forth) are called powers of ten, and they're easy to represent as exponents. Powers of ten are the result of multiplying 10 times itself any number of times.
