Decimals in real life

Without decimals you cannot really shop, weigh things, run a race, or read a thermometer. Let us see where they appear most.

Idea

Money. Rupees and paise: $\rupee 12.50$ means $12$ rupees plus $\tfrac{50}{100}$ rupees. Coins and notes are designed to give us this naturally , a $50$-paise coin is half a rupee.

Length. $1$ cm $= 10$ mm. So $5.7$ cm $= 5$ cm $+7$ mm. And $1$ m $= 100$ cm, so $2.45$ m $= 245$ cm.

Weight. $1$ kg $= 1000$ g. So $1.250$ kg $= 1250$ g.

Temperature, time, race timing. A high jumper clears $1.85$ m. A sprinter runs $100$ m in $10.32$ s. Body temperature is $37.0\,^\circ$C , the tenths place matters.

When solving real-life decimal problems, always keep units consistent. If two lengths are given as $1.2$ m and $80$ cm, convert one to the other before adding: $1.2$ m $= 120$ cm, so total is $120 + 80 = 200$ cm $= 2$ m. (Or: $80$ cm $= 0.8$ m, total $1.2 + 0.8 = 2.0$ m.)

Estimation also helps. If a bill has three items at roughly $\rupee 50$ each, expect a total near $\rupee 150$. If your decimal arithmetic gives $\rupee 1{,}500$, you know something went wrong.

Worked examples

Example 1. Convert $3.5$ kg to grams.

$3.5 \times 1000 = 3500$ g.

Example 2. A water bottle holds $1.5$ L. Express in mL.

$1.5 \times 1000 = 1500$ mL.

Example 3. A box contains $5$ items each weighing $0.75$ kg. Total weight?

$5 \times 0.75 = 3.75$ kg. (Or $5 \times 750$ g $= 3750$ g $= 3.75$ kg.)

Example 4. From $\rupee 500$, buy items costing $\rupee 89.50$, $\rupee 125.75$ and $\rupee 67.30$. Change?

Total spend: $89.50 + 125.75 + 67.30$. Add: $89.50 + 125.75 = 215.25$; $215.25 + 67.30 = 282.55$. Change: $500.00 - 282.55 = \rupee 217.45$.

Try it yourself

1. Convert $2.4$ m to cm.
2. Convert $750$ g to kg as a decimal.
3. A test tube has $0.35$ L of liquid; add $0.4$ L more. Total volume?
4. A pencil is $14.5$ cm long; another is $12.8$ cm. Difference?
5. A child weighs $32.5$ kg; an adult weighs $68$ kg. Difference?
6. Petrol costs $\rupee 105.50$ per litre. Cost of $2.5$ L?
7. A sprinter runs in $11.2$ s; another in $10.85$ s. Who is faster, and by how much?
8. Body temperature went from $37.0\,^\circ$C to $39.2\,^\circ$C. Rise?

Activity

Make a "shopping receipt" with five items. Use realistic decimal prices. Find the total, then compute the change from $\rupee 1000$.

Measure your height in metres (to two decimal places). Compare with classmates. Order the heights from shortest to tallest.