Number foundations · Topic 4 of 15

Decimals & Rounding

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Math · decimals

Know the decimal places, round by the next digit, line up points to add or subtract, count places to multiply, and shift points to divide.

01 · RoundingNext digit 5 or more → round up

02 · Add or subtractAdd/subtract: line up the decimal points

03 · MultiplyMultiply: count the total decimal places

After the point: tenths, hundredths, thousandths (each 1/10 of the last) must know

Round: next digit 5 or more → round up; under 5 → keep must know

Add/subtract: line up the decimal points (fill gaps with zeros) must know

Multiply: total decimal places in the factors = places in the answer must know

Divide by a decimal: shift both points right the same number of places must know

Rounding up a 9 carries left: 3.97 → 4.0 (nearest tenth)

Compare: pad with zeros to equal places, then compare as whole numbers

× 10, 100, 1,000: point moves right 1, 2, 3 places

Then: decimals drop later digits; whole numbers get 0s (3,649 → 3,600)

72.40 − 70.85 = 1.55 kg (zero fills the empty place)

4.5 ÷ 0.15 = 450 ÷ 15 = 30

18.346 → 18.3 (tenth) and 18.35 (hundredth)

Commonly confused

	Add / subtract	Multiply
Line up	The decimal points	No need — multiply as whole numbers
Point in the answer	Straight below the lined-up points	Count the decimal places in both factors
Zeros	Fill empty places so columns match	May need leading zeros (0.06)
Example	0.3 + 0.2 = 0.5	0.3 × 0.2 = 0.06

More digits ≠ bigger: 0.8 (0.80) > 0.75

0.3 × 0.2 = 0.06, not 0.6 (two decimal places)

Show 6 more facts

Round once from the original: 2.449 → 2.4, not 2.45 → 2.5

Money → nearest hundredth (cent); divide to thousandths first

End zeros change nothing (0.5 = 0.50); 0.05 ≠ 0.5

Say "and" at the point: 3.62 = three and sixty-two hundredths

Quotient point sits right above the dividend’s; add 0s to keep going

Negatives flip: −0.2 < −0.1

Pearl

Add or subtract: line up the points. Multiply: count the places.

Practice this topic, then test the whole section.

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