Decimals

General methodHow to add or subtract decimals

1. Write the numbers with the decimal points in a column.
2. Fill empty places with zeros (12.5 → 12.50).
3. Add or subtract as normal; the point drops straight down.

General methodHow to multiply any decimals

1. Estimate first (2.4 × 3.6 ≈ 2 × 4 = 8).
2. Ignore the points and multiply the whole numbers.
3. Count the decimal places in BOTH numbers together; give the answer that many places.

Why: \(0.3\times0.02=\tfrac3{10}\times\tfrac2{100}=\tfrac6{1000}\) - the denominators multiply, so the decimal places add.

General methodHow to divide by any decimal

1. Multiply BOTH numbers by 10, 100 or 1000 until the divisor is a whole number.
2. Divide as normal.
3. Check: dividing by a number less than 1 makes the answer bigger.

It works because \(\dfrac ab=\dfrac{10a}{10b}\): an equivalent fraction.

General methodHow to convert

1. Decimal → fraction: write it over 10, 100 or 1000 (one zero per decimal place), then simplify.
2. Fraction → decimal: top ÷ bottom.

General methodHow to type any calculation correctly

1. Brackets round the whole top and the whole bottom of a fraction.
2. A root of a sum: close the root's bracket after the whole sum: \(\sqrt{12.6+2.3^{2}}\).
3. Write down the full display (or 4-5 figures) before rounding.
4. Round to what the question asks (2 d.p., 3 s.f.); if nothing is said, 3 s.f.