Real-life decimal calculations

Outside the classroom, decimals appear most often in money, measurement and unit conversion.

Idea

Cost calculations. Multiply price by quantity. $\rupee 12.50 \times 8 = \rupee 100$.

Unit conversion. $1$ m $= 100$ cm; $1$ kg $= 1000$ g; $1$ L $= 1000$ mL. Convert by multiplying or dividing by appropriate powers of ten.

Rate problems. Often "per" indicates division. A car travels $360$ km on $40$ L of petrol: mileage $= 360 \div 40 = 9$ km/L.

Average problems. Average $=$ sum $\div$ count. Five students scored $7.5, 8.0, 6.5, 9.0, 8.5$; average $= 39.5 \div 5 = 7.9$.

Estimation, always. Before computing, check the rough scale. A weekly grocery bill should be a few thousand, not a few crore.

Worked examples

Example 1. A school buys $25$ books at $\rupee 165.50$ each. Total cost?

$165.50 \times 25 = ?$. $165.50 \times 100 = 16{,}550$; divide by $4$: $4{,}137.50$. So $\rupee 4{,}137.50$. (Alternatively $165.50 \times 25 = 165.50 \times 100 / 4$.)

Example 2. A car travels $480$ km in $6$ hours. Speed?

$480 \div 6 = 80$ km/h.

Example 3. Petrol costs $\rupee 105.50$ per litre. Cost of $2.5$ L?

$105.50 \times 2.5 = 263.75$ rupees.

Example 4. Convert $2.5$ km to cm.

$2.5$ km $\times 1000 = 2500$ m $\times 100 = 2{,}50{,}000$ cm.

Try it yourself

1. A pencil costs $\rupee 7.50$. Cost of $12$ pencils?
2. A car gives $14$ km/L. Distance on $8.5$ L?
3. Convert $5.2$ kg to g.
4. Convert $750$ mL to L.
5. A worker is paid $\rupee 4{,}500$ for $5$ days. Daily wage?
6. Three sticks of lengths $1.2, 2.4, 0.6$ m. Total?
7. A book has $245$ pages and $0.5$ cm thickness. Pages per cm?
8. Average of $4.5, 6.0, 5.5, 7.0$.

Activity

Collect $5$ receipts from your home (groceries, bills). Pick one decimal computation from each and verify it. Spot any rounding the shop did.