Decimals

A decimal is another way to write a fraction whose denominator is a power of 10 (10, 100, 1000…). The dot — the decimal point — separates whole units from parts of a unit. You meet decimals every day in Kenya: KES 50.75 on an M-Pesa receipt, 1.5 kg of unga on a duka scale, 36.6°C on a thermometer.

Place value to the right of the decimal point: each position is one tenth of the previous one — tenths (0.1), hundredths (0.01), thousandths (0.001), ten-thousandths (0.0001) and so on. So 4.327 means 4 units + 3 tenths + 2 hundredths + 7 thousandths.

Converting fractions → decimals: divide the numerator by the denominator. Some fractions terminate (1/4 = 0.25, 3/8 = 0.375); others recur — they repeat forever (1/3 = 0.333…, 2/7 = 0.285714285714…). For a recurring decimal, write a dot over the repeating digit, or three dots after it.

Converting decimals → fractions: read the decimal as it sounds, write it as a fraction, then simplify. 0.6 is "six tenths" = 6/10 = 3/5. 0.25 is "twenty-five hundredths" = 25/100 = 1/4.

Adding and subtracting decimals: line up the decimal points and add column by column, exactly like whole numbers. If one number has fewer decimal places, fill in zeros so the columns line up.

Multiplying decimals: multiply as if there were no decimal points, then count how many decimal places were in the original numbers (added together) and put that many decimal places in the answer. 0.6 × 0.4 → 6 × 4 = 24, total 2 decimal places, so the answer is 0.24.

Dividing a decimal by a whole number: divide as normal, keeping the decimal point in the same place in the answer.

Dividing a decimal by a decimal: multiply BOTH numbers by the same power of 10 until the divisor is a whole number, then divide normally. 1.2 ÷ 0.4 becomes 12 ÷ 4 = 3.

Rounding decimals: look at the digit one place to the right of where you're rounding to. If it's 5 or more, round up; if 4 or less, round down. To round 3.7894 to 2 decimal places, look at the 9 (the third decimal place) — it's 5 or more, so round the 8 up: 3.79.

Common mistakes to avoid:

• Forgetting to line up decimal points when adding or subtracting.
• Putting the decimal in the wrong place after multiplying. Always count decimal places in the inputs.
• Treating 0.5 and 0.05 as the same — the second is ten times smaller.
• Rounding repeatedly. To round 3.7894 to 2 dp, look at the 9 once, not the 4 first then the 9.

Decimals connect directly to fractions and percentages: 1/2 = 0.5 = 50%. The same value, three notations. CBC Grade 4 introduces decimals as "tenths"; Grade 5 covers hundredths and basic arithmetic; Grade 6 brings multiplying and dividing decimals and rounding; Grade 7 uses decimals inside ratio, rate and percentage problems for KPSEA.