Multiplication - Multiplication by 10, 100, and 1000

Multiplying by 10: To multiply a whole number by $10$, simply write the number and place one zero at the end. For example, $15 \times 10 = 150$. Visually, imagine the digits shifting one place to the left on a place value chart (Hundreds, Tens, Ones), which leaves the Ones place empty for a $0$ to occupy.

Multiplying by 100: To multiply a whole number by $100$, write the number and place two zeros at the end. For example, $8 \times 100 = 800$. In visual terms, the digits move two places to the left, and two zeros fill the Tens and Ones places as placeholders.

Multiplying by 1000: To multiply a whole number by $1000$, write the number and place three zeros at the end. For example, $4 \times 1000 = 4000$. This represents the digit moving three places to the left on the place value chart into the Thousands column.

Multiplying by Multiples of 10: To multiply a number by multiples of $10$ (like $20, 30, 40$), first multiply the number by the digit in the tens place, then add one zero to the product. For example, to find $5 \times 30$, multiply $5 \times 3 = 15$ and then add one zero to get $150$.

Multiplying by Multiples of 100: To multiply by multiples of $100$ (like $200, 300$), multiply the number by the digit in the hundreds place and add two zeros at the end. For $3 \times 400$, multiply $3 \times 4 = 12$ and add two zeros to get $1200$.

The Place Value Shift: When we multiply by $10, 100,$ or $1000$, the value of each digit increases. For instance, in $7 \times 10$, the $7$ which was in the 'Ones' place moves to the 'Tens' place. Visually, the number becomes ten times larger with every zero added.

Zero Counting Rule: A quick way to check your answer is to count the zeros in the multiplier ($10, 100, 1000$) and ensure the same number of zeros are added to the end of your original number.