Multiplication - Multiplication by 10, 100, and 1000

Multiplying by $10$: To multiply any whole number by $10$, simply write the number and place one zero at its end. For example, $56 \times 10 = 560$. Visually, this is equivalent to shifting every digit in the number one place to the left on a place value chart, leaving the ones place empty to be filled by a $0$.

Multiplying by $100$: To multiply a whole number by $100$, write the number and place two zeros at the end. For instance, $14 \times 100 = 1400$. In terms of place value, each digit shifts two positions to the left (e.g., a digit in the ones place moves to the hundreds place).

Multiplying by $1000$: To multiply a whole number by $1000$, write the number and place three zeros at the end. For example, $8 \times 1000 = 8000$. Imagine the number moving three steps to the left across the place value columns: Ones $\rightarrow$ Tens $\rightarrow$ Hundreds $\rightarrow$ Thousands.

Multiplying by Multiples of $10$: When multiplying by numbers like $20, 30, \dots, 90$, multiply the non-zero digits first and then append one zero. For $15 \times 30$, you calculate $15 \times 3 = 45$ and then add one zero to get $450$.

Multiplying by Multiples of $100$ and $1000$: Similar to multiples of $10$, multiply the basic numbers first and then append the total count of zeros. For $12 \times 400$, multiply $12 \times 4 = 48$ and add two zeros to get $4800$. For $5 \times 6000$, multiply $5 \times 6 = 30$ and add three zeros to get $30,000$.

The Shift Rule: Every time we multiply by a factor of $10$, the value of the number increases ten-fold. Visually, you can think of this as a number 'growing' and sliding to the left while $0$ acts as a placeholder to maintain the new, higher place values.