Last reviewed: 7 November 2026
Updated November 2026. These Grade 8 decimals notes cover converting fractions to decimals, recurring decimals and how to turn them back into fractions, rounding to decimal places and significant figures, standard form, and combined operations on decimals. Quick examples: 3/8 = 0.375 (terminating), 1/3 = 0.333… (recurring), 0.27272… = 3/11, and 45,000,000 = 4.5 × 10⁷ in standard form.
The examples and questions are original practice for Kenyan junior school learners, not an official paper. For the other Grade 8 maths topics, see our Grade 8 mathematics revision guide and the Grade 8 notes hub.
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What the Grade 8 Curriculum Covers
Decimals is a sub-strand under Numbers in the Kenya Institute of Curriculum Development’s Grade 8 Mathematics design. Learners convert fractions to decimals, identify recurring decimals and convert them to fractions, round to decimal places and significant figures, write numbers in standard form, and carry out combined operations on decimals. The design is listed on the KICD Grade Eight curriculum designs page.
Fractions to Decimals
Divide the numerator by the denominator, as shown in OpenStax Prealgebra’s section on decimals and fractions.
- 3/8 = 3 ÷ 8 = 0.375. The division ends, so this is a terminating decimal.
- 5/11 = 0.454545… The digits 45 repeat forever, so this is a recurring decimal, written 0.45 with dots (or a bar) over the 4 and 5.
A fraction in its simplest form gives a terminating decimal only when its denominator has no prime factors other than 2 and 5. So 7/20 terminates (20 = 2² × 5) but 1/6 recurs (6 = 2 × 3).
Recurring Decimals to Fractions
One repeating digit
Let x = 0.777… Then 10x = 7.777… Subtract: 9x = 7, so x = 7/9.
Two repeating digits
Let x = 0.272727… Then 100x = 27.2727… Subtract: 99x = 27, so x = 27/99 = 3/11.
Repeating part after a non-repeating digit
Let x = 0.1666… Then 10x = 1.666… and 100x = 16.666… Subtract: 90x = 15, so x = 15/90 = 1/6.
Rule of thumb: multiply by 10 for each repeating digit so that the repeating parts line up, then subtract.
Decimal Places and Significant Figures
- Decimal places count digits after the decimal point. 7.6482 to 2 d.p. = 7.65.
- Significant figures count from the first non-zero digit. 23,481 to 3 s.f. = 23,500. 0.004562 to 2 s.f. = 0.0046 (leading zeros are not significant).
Zeros between non-zero digits are significant: 40,507 has 5 significant figures.
Standard Form
A number in standard form is written as A × 10ⁿ, where 1 ≤ A < 10 and n is a whole number. This is the same as scientific notation in OpenStax Prealgebra’s section on scientific notation.
- 45,000,000 = 4.5 × 10⁷ (the point moves 7 places left).
- 0.00072 = 7.2 × 10⁻⁴ (the point moves 4 places right).
- 3.06 × 10⁵ = 306,000.
Writing 45 × 10⁶ is not standard form, because 45 is not between 1 and 10.
Combined Operations on Decimals
Follow the usual order: brackets, division and multiplication, then addition and subtraction.
Example: (2.4 × 0.5 + 1.8) ÷ 0.3 = (1.2 + 1.8) ÷ 0.3 = 3.0 ÷ 0.3 = 10.
To divide by a decimal, multiply both numbers by a power of 10 to make the divisor whole: 3.0 ÷ 0.3 = 30 ÷ 3 = 10.
Real-life example
In this made-up example, a farmer sells 12.5 kg of beans at KSh 140.80 per kg and pays KSh 75.50 transport. Net income = 12.5 × 140.80 − 75.50 = 1,760 − 75.50 = KSh 1,684.50.
Original Practice Questions With Worked Answers
- Convert 7/16 to a decimal. 0.4375.
- Write 0.555… as a fraction. 5/9.
- Write 0.363636… as a fraction in its simplest form. 36/99 = 4/11.
- Round 0.08349 to 3 significant figures. 0.0835.
- Write 0.000305 in standard form. 3.05 × 10⁻⁴.
- Evaluate 6.4 ÷ 0.08 − 1.5 × 4. 80 − 6 = 74.
Cover the answers and attempt each question first. For timed practice, use the Grade 8 revision papers or the Grade 8 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
What is a recurring decimal?
A decimal in which one or more digits repeat forever, such as 0.333… or 0.142857142857…
How do you convert a recurring decimal to a fraction?
Let x equal the decimal, multiply by a power of 10 so the repeating parts line up, subtract the two equations and solve for x.
What is standard form?
A way of writing numbers as A × 10ⁿ, where A is at least 1 and less than 10.
Are zeros significant figures?
Leading zeros are not; zeros between non-zero digits are. Trailing zeros depend on how the number was rounded.