Multiplying and Dividing by 10, 100 and 1000
Multiplying by ten
Multiplying a whole number by 10 has a neat effect: every digit moves one place to the left, and a zero fills the empty ones place. So 37 times 10 is 370, and 8 times 10 is 80. This is not a trick to memorise but a direct result of place value — making a number ten times bigger shifts each digit into the next column up. Year 4 multiplies and divides by 10, 100 and 1000 this way, mentally and without a calculator, by understanding the shift rather than counting on fingers.
Why the digits move
The shift happens because of what place value means. Each column is ten times the one to its right: ones, tens, hundreds, thousands. Multiplying by 10 makes every digit ten times bigger, so a digit worth 4 tens becomes worth 4 hundreds — it moves up one column. The zero that appears in the ones place is not added arbitrarily; it holds the now-empty column. Seeing the shift as digits climbing the place-value columns, rather than as a rule about adding zeros, is what makes dividing and larger powers make sense too.
Dividing by ten
Dividing by 10 is the exact reverse: every digit moves one place to the right, becoming ten times smaller. So 250 divided by 10 is 25, and 80 divided by 10 is 8. A digit worth 5 tens becomes worth 5 ones; the columns step down instead of up. Because division undoes multiplication, the digits simply travel the opposite way along the place-value columns. Understanding both directions — left for times, right for divide — means a child can handle either operation by the same place-value idea.
By a hundred and a thousand
Multiplying by 100 or 1000 works the same way, just further. 100 is ten tens, so multiplying by 100 shifts every digit two places left; 1000 shifts three places. Thus 5 times 100 is 500, and 7 times 1000 is 7000. The number of places to shift is exactly the number of zeros in the multiplier. This connects all the powers of 10 into one idea: each zero means another ten times bigger, another column to climb. The same holds for dividing, shifting right by the number of zeros.
Counting the zeros
This gives a quick and reliable rule: the number of zeros in 10, 100 or 1000 tells you how many places to shift. One zero, one place; two zeros, two places; three zeros, three places. The rule is fast, but it is worth remembering why it works — each zero stands for another factor of ten, another column. A child who knows both the shortcut and the place-value reason behind it can multiply and divide by powers of 10 confidently, and will not be fooled into simply tacking zeros onto the wrong kind of number.
Powers of 10 together
Pulling the unit together, multiplying or dividing by a power of 10 always shifts the digits along the place-value columns: left for multiplying, right for dividing, by as many places as the multiplier has zeros. A table captures it — times 10, 100, 1000 shift one, two, three places left, and dividing shifts right. With the place-value reason understood and the count-the-zeros shortcut in hand, a child can multiply and divide whole numbers by 10, 100 and 1000 mentally and without a calculator, a key skill for larger calculations and for understanding our whole base-ten number system.