These questions ask you to scale a decimal by a power of ten, reverse that scaling, or recognise an equivalent expression. Decide two things before moving the point: whether the value should grow or shrink, and how many places the stated factor requires.
Use direction, then count places
Write an unwritten decimal point after a whole number and add placeholder zeros only when the point needs room to move. Multiplication by a power greater than one moves the point right; division by that power moves it left. The number of zeros in 10, 100 or 1000 gives one, two or three moves. For example, 2.45 × 10 = 24.5, while 380 ÷ 100 = 3.8. Check the size: the first result must be larger and the second smaller.
| Operation | Equivalent view | Point movement |
|---|---|---|
| Multiply by 10, 100 or 1000 | Scale up by the stated power | Right by one, two or three places |
| Divide by 10, 100 or 1000 | Split into the stated number of equal parts | Left by one, two or three places |
| Multiply by 0.1 or 0.01 | Divide by 10 or 100 | Left by one or two places |
| Divide by 0.1 | Multiply by 10 | Right by one place |
A decimal multiplier less than one reverses the usual multiplication direction. For example, 1.46 × 0.1 = 0.146 because taking one tenth is the same as dividing by ten. Keep the equivalence in words before shifting anything: multiply by one tenth means find one tenth of the starting value.
Avoid these scaling traps
| Tempting route | How to reject it |
|---|---|
| Move in the wrong direction | Predict the size first. Multiplying by a power greater than one grows the value, while dividing by it shrinks the value. |
| Move one place for every power of ten | Count the zeros in the power: 100 needs two moves and 1000 needs three. |
| Treat multiplication by 0.1 like multiplication by 10 | One tenth is less than one, so the result must shrink. Replace multiplication by 0.1 with division by 10. |
| Append or remove zeros without tracking the decimal point | Zeros are placeholders, not the method. Move the point the required distance, adding placeholders only if a place is empty. |
Try it
A microscope scale multiplies a reading of 4.07 by 100. Enter the resulting number.
A 720-unit quantity is split into 100 equal parts. Enter the value of one part.
Enter the result of 9.05 divided by 10.