These questions use decimals in prices, change, lengths, masses, and rates per unit. Begin by naming the quantity you need, then choose the operation or power-of-ten conversion that produces that unit.
Match the method to the required unit
Money written in dollars and hundredths uses two places after the point. Writing 4.6 dollars as 4.60 dollars adds a trailing zero without changing the value. For addition or subtraction, align the decimal points and pad missing places with zeros. For example, change from 10.00 dollars after spending 3.45 dollars is found by 10.00 - 3.45 = 6.55 dollars.
Metric conversions use fixed powers of ten. Multiply metres by 100 to get centimetres, so 1.63 metres becomes 163 centimetres. Multiply kilograms by 1000 to get grams, so 0.27 kilograms becomes 270 grams. Going back to the larger unit reverses the operation and divides by the same factor.
For rates, write the required unit as a guide. Price per kilogram means total dollars ÷ kilograms. For example, 8.40 dollars for 3.5 kilograms gives 8.40 ÷ 3.5 = 2.40 dollars per kilogram. If the price per kilogram and number of kilograms are known, reverse the relationship: total cost equals unit price × quantity. At 1.40 dollars per kilogram, 3 kilograms cost 1.40 × 3 = 4.20 dollars.
| Required quantity | Method |
|---|---|
| Money in dollars and hundredths | Show two decimal places; a trailing zero preserves value. |
| Change or remaining measure | Subtract with decimal points aligned and zeros padded. |
| Centimetres from metres | Multiply by 100. |
| Grams from kilograms | Multiply by 1000. |
| Price per unit | Divide total price by quantity. |
| Total cost | Multiply unit price by quantity. |
Common wrong turns
| Tempting route | How to reject it |
|---|---|
| Insert a zero between the point and an existing decimal digit | That moves the digit into a smaller place and changes the amount. Add money's display zero only after the last non-zero decimal digit. |
| Multiply total price by mass to find a unit price | Per kilogram asks for the cost of one kilogram. Divide total dollars by the number of kilograms. |
| Compare total prices without comparing quantities | A smaller pack may cost less overall but more per kilogram. Calculate each unit price before comparing. |
| Move the point the wrong number of places in a metric conversion | Name the conversion factor first: 100 for metres to centimetres and 1000 for kilograms to grams. Then check that conversion to a smaller unit gives more units, not fewer. |
| Apply a familiar operation without checking the target value | Carry out the arithmetic and retain two-place money notation. A calculation's appearance alone does not show that it reaches the requested amount. |
Try it
A customer pays 20 dollars for an item costing 13.65 dollars. Enter the amount of change in dollars.
A shelf is 2.75 metres long. Enter its length in centimetres.
A 4.5-kilogram bag costs 9.90 dollars. Enter the price per kilogram in dollars.